AChacon006/Physics

1{"id": 1, "title": "Constant Velocity (Basic)", "question": "A runner jogs in a straight line at a constant speed of 3.5 m/s for 12 minutes.\n(a) How far does the runner travel during this time?\n(b) How many kilometers is that?"}2{"id": 2, "title": "Constant Acceleration (Introductory)", "question": "A car accelerates uniformly from rest to a speed of 20 m/s in 8 seconds.\n(a) What is the car’s acceleration?\n(b) How far does it travel during this time?"}3{"id": 3, "title": "Vertical Motion (Intermediate)", "question": "A ball is thrown straight upward with an initial velocity of 15 m/s.\n(a) How long does it take to reach its highest point?\n(b) What is the maximum height reached by the ball?\n(c) How long is the ball in the air before it hits the ground?"}4{"id": 4, "title": "Kinematic Graphs (Intermediate)", "question": "A position-time graph shows a piecewise linear path:\n● From t = 0 to t = 5 s, the object moves from x = 0 m to x = 20 m.\n● From t = 5 s to t = 10 s, the object remains at rest.\n● From t = 10 s to t = 15 s, it returns to x = 0 m.\n(a) Sketch the velocity-time graph for this motion.\n(b) What is the object’s average velocity over the entire trip?"}5{"id": 5, "title": "Two-Object Motion (Advanced)", "question": "A bicyclist traveling at 5 m/s passes a pedestrian who is walking at 1.5 m/s. At the moment they\nmeet, the pedestrian begins to accelerate at 0.5 m/s².\n(a) How long will it take the pedestrian to catch up to the bicyclist?\n(b) How far will the pedestrian have traveled in that time?"}6{"id": 6, "title": "Nonzero Initial Conditions (Advanced)", "question": "A car moving at 25 m/s begins to decelerate uniformly at 3 m/s².\n(a) How far does the car travel before coming to a stop?\n(b) How long does it take to come to a stop?\n(c) Sketch a velocity-time and acceleration-time graph."}7{"id": 7, "title": "Relative Motion (Challenge)", "question": "A train is moving at 30 m/s relative to the ground. A passenger walks toward the front of the\ntrain at 2 m/s relative to the train. Another observer is standing on a platform.\n(a) What is the passenger's speed relative to the platform?\n(b) If the train is 180 m long, how long does it take the passenger to walk from the rear to the\nfront as measured by the observer on the platform?\nKINEMATICS TEST PROBLEMS: 2D MOTION & PROJECTILES"}8{"id": 8, "title": "Vector Components (Basic 2D Motion)", "question": "A boat crosses a 100-meter-wide river flowing east at 2 m/s. The boat moves directly north at 3\nm/s relative to the water.\n(a) How long does it take the boat to reach the opposite bank?\n(b) How far downstream is the boat when it reaches the far shore?\n(c) What is the magnitude and direction of the boat’s velocity relative to the ground?"}9{"id": 9, "title": "Projectile Launched Horizontally (Introductory Projectile)", "question": "A ball rolls off a horizontal table that is 1.25 m high and lands 2.50 m from the base of the table.\n(a) How long was the ball in the air?\n(b) What was its horizontal speed as it left the table?\n(c) What was the speed just before impact?"}10{"id": 10, "title": "Angle-Launched Projectile (Intermediate)", "question": "A soccer ball is kicked with an initial speed of 18 m/s at an angle of 35° above the horizontal.\n(a) What are the horizontal and vertical components of the initial velocity?\n(b) How long does the ball remain in the air?\n(c) What is the range (horizontal distance traveled)?\n(d) What is the maximum height reached?"}11{"id": 11, "title": "Maximum Range Conditions (Conceptual + Math)", "question": "A projectile is launched from the ground with a fixed speed of 25 m/s.\n(a) At what angle should it be launched to achieve maximum range?\n(b) What is that maximum range?\n(c) How long is the projectile in the air at that angle?"}12{"id": 12, "title": "Uneven Height Launch (Advanced)", "question": "A rock is thrown from a cliff 45 m above the ground. It is launched with a speed of 12 m/s at an\nangle of 20° above the horizontal.\n(a) How long is the rock in the air before it hits the ground?\n(b) What is the horizontal distance from the base of the cliff where it lands?\n(c) What is the speed and direction of the rock just before it hits the ground?"}13{"id": 13, "title": "Two-Projectile Collision (Challenge)", "question": "Two students are standing 50 m apart. At the same time, Student A throws a ball horizontally at\n10 m/s, and Student B throws a ball at the same height at 15 m/s and 37° above the horizontal,\naimed toward Student A.\n(a) Will the balls collide in the air?\n(b) If yes, how high above the ground do they collide?\nKINEMATICS TEST PROBLEMS: CHALLENGING & CREATIVE"}14{"id": 14, "title": "Motion with a Time-Dependent Acceleration", "question": "A particle starts from rest at the origin. Its acceleration increases linearly with time according to\nthe equation a(t)=4ta(t) = 4ta(t)=4t m/s².\n(a) Find an expression for the velocity as a function of time.\n(b) Find an expression for position as a function of time.\n(c) How far has it traveled after 3 seconds?"}15{"id": 15, "title": "Disappearing Tunnel", "question": "A car is driving through a tunnel of length 800 m at a constant speed of 25 m/s. Suddenly, the\ntunnel begins collapsing from the entrance inward at a rate of 5 m/s.\n(a) Will the car make it out in time?\n(b) If not, how far into the tunnel does it get before being caught?"}16{"id": 16, "title": "Coordinated Cliff Launch", "question": "Two stones are launched simultaneously from the top of a 60 m cliff:\n● Stone A is thrown horizontally at 12 m/s.\n● Stone B is thrown upward at a 30° angle with a speed of 20 m/s.\n(a) Do the stones collide in midair?\n(b) If so, at what time and coordinates?"}17{"id": 17, "title": "Velocity Match in Air", "question": "A ball is kicked upward at 20 m/s at an angle of 45° with the horizontal. At the exact same time,\nanother ball is dropped from rest from a height of 15 m.\n(a) Is there a time during flight when both balls have the same speed (not direction)?\n(b) If yes, at what time and what is the value of that speed?"}18{"id": 18, "title": "Moving Target Problem", "question": "A dart is thrown at a monkey hanging from a branch 12 meters above the ground and 18\nmeters horizontally from the dart thrower. The instant the dart is thrown, the monkey lets go and\nbegins to fall.\nAssuming the dart is aimed directly at the monkey and air resistance is negligible:\n(a) What minimum speed must the dart be thrown at to hit the monkey?\n(b) Would the dart still hit the monkey if thrown with a greater speed?"}19{"id": 19, "title": "Kinematics Puzzle – Equal Heights", "question": "A ball is thrown upward from the ground with a speed of 20 m/s. At the same time, a second\nball is dropped from a height of 15 meters.\n(a) At what time do the two balls pass each other?\n(b) At what height above the ground does this occur?\n(c) What is the relative speed between the two balls at that moment?"}20{"id": 20, "title": "Time-Shifted Chase", "question": "Runner A passes a point at t = 0 moving at a constant speed of 4.0 m/s.\nRunner B starts 6 seconds later at the same point and accelerates uniformly at 1.2 m/s².\n(a) Will Runner B catch Runner A?\n(b) If so, at what time and how far from the start point?\nDYNAMICS TEST PROBLEMS"}21{"id": 21, "title": "Newton’s First Law (Basic)", "question": "A hockey puck slides across frictionless ice at 6.0 m/s. No forces are acting on it after it is hit.\n(a) What is the acceleration of the puck?\n(b) How far does it travel in 5.0 seconds?"}22{"id": 22, "title": "Weight and Normal Force (Basic)", "question": "A 4.0 kg box rests on a flat horizontal surface.\n(a) What is the weight of the box?\n(b) What is the normal force acting on it?"}23{"id": 23, "title": "Force and Acceleration (Introductory)", "question": "A 10 kg crate is pulled across a frictionless surface by a horizontal force of 25 N.\n(a) What is the acceleration of the crate?\n(b) How far does it move in 4.0 seconds?"}24{"id": 24, "title": "Inclined Plane (Intermediate)", "question": "A 5.0 kg object is placed on a frictionless 30° incline.\n(a) What is the acceleration of the object down the incline?\n(b) What is the normal force acting on the object?"}25{"id": 25, "title": "Tension in a Rope (Intermediate)", "question": "Two blocks are connected by a light string on a horizontal, frictionless surface. Block A has\nmass 3.0 kg, block B has mass 2.0 kg. A horizontal force of 20 N pulls the system.\n(a) What is the acceleration of the system?\n(b) What is the tension in the string between the blocks?"}26{"id": 26, "title": "Elevator Forces (Intermediate Conceptual)", "question": "You stand on a bathroom scale inside an elevator. Your mass is 70 kg.\n(a) What does the scale read when the elevator accelerates upward at 2 m/s²?\n(b) What does it read when accelerating downward at 2 m/s²?\n(c) What does it read when moving at constant velocity?"}27{"id": 27, "title": "Friction on a Ramp (Challenging)", "question": "A 6.0 kg box slides down a 25° incline. The coefficient of kinetic friction between the box and\nthe incline is 0.20.\n(a) What is the net force acting on the box?\n(b) What is its acceleration?"}28{"id": 28, "title": "Atwood Machine (Classic Intermediate)", "question": "Two masses, 4.0 kg and 2.0 kg, hang over a pulley. Assume the pulley is massless and\nfrictionless.\n(a) What is the acceleration of the system?\n(b) What is the tension in the rope?"}29{"id": 29, "title": "Pushing with Friction (Advanced)", "question": "You push a 10.0 kg crate with a horizontal force of 50 N across a floor where the coefficient of\nkinetic friction is 0.30.\n(a) What is the frictional force?\n(b) What is the net force and resulting acceleration?"}30{"id": 30, "title": "Modified Atwood (Advanced Creative)", "question": "Mass A (5.0 kg) rests on a table connected by a string over a pulley to hanging mass B (3.0\nkg). The table is frictionless.\n(a) What is the acceleration of the system?\n(b) What is the tension in the string?\n(c) What happens if B’s mass increases slightly? Explain physically."}31{"id": 31, "title": "Multi-Block System with Friction (Advanced)", "question": "Three blocks (m₁ = 2 kg, m₂ = 3 kg, m₃ = 5 kg) are lined up on a horizontal surface with μ(cid:0) =\n0.1 and pushed by a 50 N force on the 2 kg block.\n(a) What is the acceleration of the system?\n(b) What is the contact force between m₁ and m₂?\n(c) What is the contact force between m₂ and m₃?\nADVANCED & CREATIVE DYNAMICS PROBLEMS"}32{"id": 32, "title": "Double Ramp Surprise", "question": "A frictionless track consists of two ramps: one ascending at 30° and the other descending at\n45°, connected at the top by a flat horizontal section. A block of mass 2 kg is released from rest\nat the bottom of the 30° ramp, slides up and over the top, and then descends the 45° ramp.\n(a) What is the acceleration of the block on each ramp?\n(b) How long does it take the block to reach the top of the 30° ramp if the ramp is 3.0 m long?\n(c) How fast is it going when it reaches the bottom of the 45° ramp?"}33{"id": 33, "title": "Slipping and Sliding Stack", "question": "A small block of mass mmm rests on top of a larger block of mass 4m4m4m, which sits on a\nfrictionless table. The coefficient of static friction between the blocks is μs=0.4\\mu_s =\n0.4μs =0.4. A horizontal force FFF is applied to the bottom block.\n(a) What is the maximum value of FFF that can be applied without the top block sliding?\n(b) What is the acceleration of the system at that point?"}34{"id": 34, "title": "Tension Tug-of-War", "question": "A rope passes over a frictionless pulley and connects two masses: a 5.0 kg block on a\nhorizontal table and a 3.0 kg hanging mass. The table has μ(cid:0) = 0.2. Suddenly, the 5.0 kg block\nis pulled sideways (perpendicular to the rope direction) with a strong instantaneous horizontal\nkick.\n(a) Immediately after the kick, what happens to the tension in the rope?\n(b) Will the 3.0 kg mass still accelerate downward, or does the system stall?"}35{"id": 35, "title": "Block and Wall Trick", "question": "A block of mass mmm is pressed against a vertical wall by a horizontal force FFF. The\ncoefficient of static friction between the block and the wall is μs\\mu_sμs .\n(a) Derive the condition for FFF such that the block does not fall.\n(b) Explain physically what happens if FFF is too small, and what happens if FFF is much larger\nthan needed."}36{"id": 36, "title": "Two Forces, One Mystery", "question": "A 6.0 kg block is pushed across a rough surface by two people: one applies a 30 N force at 30°\nabove horizontal, and the other applies a 25 N force at 20° below horizontal. The coefficient of\nkinetic friction is 0.15.\n(a) What is the net vertical force on the block?\n(b) What is the normal force?\n(c) What is the block’s acceleration?"}37{"id": 37, "title": "Falling Ladder Thought Experiment", "question": "A uniform ladder of length LLL leans against a frictionless vertical wall. The bottom of the\nladder rests on rough ground. It begins to slip.\n(a) As it slips, is the center of mass accelerating horizontally, vertically, or both?\n(b) Describe the net force and torque acting on the ladder as it falls.\n(c) Can Newton’s Laws alone predict the angle at which the ladder loses contact with the wall?"}38{"id": 38, "title": "Double Pulley Trap", "question": "A double Atwood machine is set up: Block A (mass 3 kg) hangs on one end of a rope over\nPulley P1. The other end of the rope is connected to Pulley P2, which has block B (mass 1 kg)\nhanging from one side and block C (mass 2 kg) from the other. Assume all pulleys and strings\nare massless and frictionless.\n(a) Find the acceleration of block A.\n(b) Which direction do each of the blocks accelerate?"}39{"id": 39, "title": "Rocket Cart with Sand Loss", "question": "A cart of mass 10 kg starts at rest on a frictionless track. It contains a tank that ejects sand\nbackward at 5 m/s relative to the cart at a constant rate of 0.1 kg/s.\n(a) What is the speed of the cart after 20 seconds?\n(b) What is the net external force acting on the cart?"}40{"id": 40, "title": "Walking on a Boat", "question": "A person of mass 60 kg walks from one end of a stationary 200 kg flatboat to the other end (8\nm long) at 1.5 m/s relative to the boat.\n(a) How far does the boat move by the time the person reaches the far end?\n(b) What is the velocity of the boat during the walk?\nSIMPLE CIRCULAR MOTION: CENTRIPETAL ACCELERATION &\nKINEMATICS"}41{"id": 41, "title": "Basic Centripetal Acceleration", "question": "A 0.50 kg object moves in a circle of radius 2.0 m at a constant speed of 4.0 m/s.\n(a) What is the object's centripetal acceleration?\n(b) How long does it take to complete one full revolution?"}42{"id": 42, "title": "Angular Velocity Conversion (Basic)", "question": "A CD spins at 720 revolutions per minute (rpm).\n(a) What is the angular velocity in radians per second?\n(b) How long does it take to complete one revolution?"}43{"id": 43, "title": "Linear and Angular Velocity (Introductory)", "question": "A bug is sitting 0.15 m from the center of a rotating record spinning at 33 ⅓ rpm.\n(a) What is the bug’s linear speed?\n(b) What is the centripetal acceleration of the bug?"}44{"id": 44, "title": "Going in Circles (Intermediate)", "question": "A child on a merry-go-round moves in a circle of radius 3.5 m. If the ride makes one full rotation\nevery 6.0 seconds:\n(a) What is the child’s linear speed?\n(b) What is their centripetal acceleration?"}45{"id": 45, "title": "Two Riders, Different Radii (Intermediate Conceptual)", "question": "Two people sit on opposite ends of a rotating disc. Person A is 1.0 m from the center, and\nPerson B is 2.0 m from the center. The disc rotates at a constant rate.\n(a) Who has the greater linear speed?\n(b) Who has the greater angular speed?\n(c) Who experiences greater centripetal acceleration?"}46{"id": 46, "title": "Quarter Turn Puzzle (Intermediate)", "question": "An object moves in a circle of radius 1.2 m at 3.0 m/s.\n(a) How much time does it take to move 90° around the circle?\n(b) What distance does it travel in that time?"}47{"id": 47, "title": "Speed from Acceleration (Reverse Problem)", "question": "A ball is whirling in a circle on a string. Its radius is 0.75 m, and the centripetal acceleration is\nmeasured to be 9.0 m/s².\n(a) What is the speed of the ball?\n(b) How long does it take to complete one full circle?"}48{"id": 48, "title": "Comparing Orbits (Creative)", "question": "Two satellites orbit Earth in circular paths. Satellite A is in a 300 km orbit, and satellite B is in a\n600 km orbit. Assume constant speed and circular paths.\n(a) Which satellite takes longer to complete an orbit?\n(b) Which satellite has greater centripetal acceleration?\n(c) Which one has a greater linear speed?"}49{"id": 49, "title": "Pie Slice Racer (Advanced Geometry)", "question": "An object moves in a circular arc that spans a central angle of 60° in 4.0 seconds. The radius of\nthe circle is 1.5 m.\n(a) What is its average linear speed?\n(b) What is its angular speed in rad/s?\n(c) What is its centripetal acceleration at that speed?"}50{"id": 50, "title": "Nonuniform Arc Entry (Creative Conceptual)", "question": "An object begins to move along a circular arc of radius 2.0 m from rest, speeding up uniformly\nuntil it reaches 4.0 m/s at the halfway point (i.e. after covering a quarter circle).\n(a) What is the average linear speed during that motion?\n(b) How long did it take to reach the halfway point?\n(c) What was the average centripetal acceleration over the interval?\nCHALLENGING & CONCEPTUAL CIRCULAR MOTION PROBLEMS\n(No torque. Focus on a(cid:0) = v²/r and circular kinematics)"}51{"id": 51, "title": "The Floor Drops Out", "question": "You are inside a spinning carnival ride: a large vertical cylinder rotates until you are pressed\nagainst the wall, and then the floor drops out. The radius is 2.5 m, and the ride spins at a speed\nsuch that your body experiences a centripetal acceleration of 25 m/s².\n(a) What is your speed as the ride spins?\n(b) What minimum coefficient of static friction is needed to keep you from sliding down once the\nfloor is gone?\n(c) What direction is the net force acting on you?"}52{"id": 52, "title": "Upside Down Over the Hill", "question": "A car goes over the top of a circular hill with a radius of 50 m while traveling at 20 m/s.\n(a) What is the centripetal acceleration at the top of the hill?\n(b) What would a scale inside the car read if the driver has a mass of 70 kg?\n(c) At what speed would the driver feel \"weightless\"?"}53{"id": 53, "title": "Airplane Turn with Banking", "question": "An airplane flies in a horizontal circle of radius 200 m while tilted at a bank angle of 30° to keep\nlevel flight. Ignore lift equations.\n(a) What is the speed required to maintain the turn?\n(b) What provides the centripetal acceleration in this case?\n(c) What would happen if the plane slowed down during the turn?"}54{"id": 54, "title": "Tension at the Bottom", "question": "A mass is swung in a vertical circle at the end of a string. At the bottom of the circle, the speed\nis 6.0 m/s and the radius is 0.8 m.\n(a) What is the centripetal acceleration at that point?\n(b) If the mass is 1.2 kg, what is the tension in the string at the bottom?\n(c) Is the tension greater at the bottom or the top of the swing? Explain why without using\ntorque."}55{"id": 55, "title": "Gravity and Circular Orbits", "question": "The International Space Station orbits Earth at about 400 km above the surface. Assume a\ncircular orbit with radius 6.77 × 10⁶ m.\n(a) What is its orbital speed?\n(b) What is its centripetal acceleration?\n(c) Is the ISS truly \"weightless\"? Explain conceptually why astronauts feel weightless, even\nthough gravity is still acting on them."}56{"id": 56, "title": "Ride the Loop", "question": "A rollercoaster car enters a vertical loop of radius 10.0 m. Assume frictionless tracks and\nconservation of energy.\n(a) What minimum speed must the car have at the top of the loop to stay on the track?\n(b) From what minimum height must it be released to achieve this speed at the top?\n(c) At the bottom of the loop, how does the normal force compare to the weight? Explain using\nnet force and centripetal acceleration."}57{"id": 57, "title": "The Lost Ball", "question": "A ball tied to a string is spun in a horizontal circle on a frictionless table. Suddenly, the string\nsnaps.\n(a) What happens to the ball's path immediately after the string breaks?\n(b) What force was acting on the ball before the string broke?\n(c) Is there any force pushing the ball outward while it's spinning?"}58{"id": 58, "title": "Planet Spin-Off", "question": "A hypothetical planet spins so fast that an object on the equator becomes weightless.\n(a) Derive an expression for the minimum angular speed ω\\omegaω at which this happens in\nterms of ggg and RRR.\n(b) What is the linear speed of a person standing at the equator at that point?\n(c) Would the person feel \"flung off\"? Why or why not?"}59{"id": 59, "title": "Loop-the-Loop Hang Time", "question": "In a skate park, a loop-the-loop has radius 2.0 m. A skateboarder of mass 60 kg enters the loop\nfrom a height of 5.5 m above the bottom.\n(a) Does the skateboarder make it all the way around without falling?\n(b) What is their speed at the top of the loop?\n(c) What normal force acts on them at the top?"}60{"id": 60, "title": "Constant Acceleration Spiral Track", "question": "A car accelerates uniformly along a spiral track, increasing its speed while circling inward. At\none instant, it is moving at 12 m/s in a circle of radius 25 m.\n(a) What is the magnitude of its centripetal acceleration at that moment?\n(b) If its speed is increasing at 2.0 m/s², what is its total acceleration (magnitude and direction)?\n(c) Draw and label the direction of centripetal and tangential acceleration vectors.\nGRAVITATION, GEOSYNCHRONOUS ORBITS & KEPLER’S LAW\nPROBLEMS"}61{"id": 61, "title": "Gravity at Earth’s Surface (Basic)", "question": "The mass of Earth is 5.97×10245.97 \\times 10^{24}5.97×1024 kg, and its radius is\n6.37×1066.37 \\times 10^66.37×106 m.\n(a) Use Newton’s Law of Gravitation to calculate ggg at Earth’s surface.\n(b) Compare your result to the standard value of 9.8 m/s²."}62{"id": 62, "title": "Weight in Orbit (Introductory)", "question": "An astronaut orbits Earth in the ISS at a height of 400 km above the surface.\n(a) What is the gravitational acceleration at that altitude?\n(b) If the astronaut has a mass of 70 kg, what is their “weight” at that altitude (magnitude of\ngravitational force)?\n(c) Why do they feel weightless?"}63{"id": 63, "title": "Period of a Satellite (Kepler/Gravitation)", "question": "A satellite orbits Earth in a circular orbit at 900 km altitude.\n(a) Find the orbital radius.\n(b) Use Newton’s version of Kepler’s Third Law to find its orbital period.\n(c) What is the satellite’s orbital speed?"}64{"id": 64, "title": "Geosynchronous Orbit (Standard Classic)", "question": "A geosynchronous satellite must orbit with a period of exactly 24 hours.\n(a) Derive the radius of its orbit.\n(b) How high above Earth’s surface is it?\n(c) What is its orbital speed?"}65{"id": 65, "title": "Moon Orbiting Earth", "question": "The Moon orbits Earth at a distance of about 3.84×1083.84 \\times 10^83.84×108 m and has a\nperiod of 27.3 days.\n(a) Use this data to estimate the mass of Earth.\n(b) What is the gravitational force between the Earth and the Moon?\n(c) What is the speed of the Moon in its orbit?"}66{"id": 66, "title": "Kepler’s Third Law Conceptual", "question": "Planet A orbits its star at 1 AU with a period of 1 Earth year. Planet B orbits the same star at 4\nAU.\n(a) What is the period of Planet B’s orbit?\n(b) If Planet C has a period of 8 years, how far from the star is it?"}67{"id": 67, "title": "Gravity on Other Planets (Conceptual Reasoning)", "question": "Planet X has twice the mass of Earth and the same radius.\n(a) How does ggg on Planet X compare to ggg on Earth?\n(b) How would the weight of a 70 kg astronaut change on Planet X?"}68{"id": 68, "title": "Orbital Energy Transfer (Creative)", "question": "A satellite in low Earth orbit fires a rocket and moves into a higher circular orbit.\n(a) In the new orbit, is the satellite’s speed higher, lower, or the same?\n(b) Is the total mechanical energy of the satellite greater or less than before?\n(c) Explain your answers using gravitational potential and kinetic energy."}69{"id": 69, "title": "Launch to Orbit (Application)", "question": "To place a satellite into a circular orbit 500 km above Earth, it must reach orbital speed.\n(a) What is the minimum speed required at that altitude?\n(b) What is the total energy (kinetic + gravitational) per kilogram of satellite in orbit?\n(c) How does this compare to the energy needed to lift the satellite to that height without orbit?"}70{"id": 70, "title": "Binary Star System (Challenging)", "question": "Two stars of equal mass orbit each other at a separation of 8.0 × 10¹⁰ m.\n(a) Derive the expression for the period of their orbit using Newton’s version of Kepler’s law.\n(b) If each star has a mass of 2.0×10302.0 \\times 10^{30}2.0×1030 kg, what is the period of\ntheir orbit?\n(c) Describe what would happen to the period if their separation doubled.\nWORK, ENERGY, AND POWER PROBLEMS\n(Increasing in difficulty, with multi-concept integration)"}71{"id": 71, "title": "Work by a Constant Force (Basic)", "question": "A 12 N force pushes a 3.0 kg box along a frictionless surface for 5.0 meters.\n(a) How much work is done by the force?\n(b) What is the box’s final speed if it started from rest?"}72{"id": 72, "title": "Work at an Angle (Introductory)", "question": "A 20 N force pulls a box at 30° above horizontal for 6.0 meters across a frictionless floor.\n(a) How much work is done by the force?\n(b) If the box has a mass of 4.0 kg and starts from rest, what is its final speed?"}73{"id": 73, "title": "Gravitational Potential Energy (Conceptual + Numeric)", "question": "A 70 kg climber ascends 25 m up a cliff.\n(a) How much gravitational potential energy does she gain?\n(b) If she climbs at a constant speed in 60 seconds, what is her average power output?"}74{"id": 74, "title": "Kinetic Energy and Speed (Intermediate)", "question": "A car of mass 800 kg increases its speed from 10 m/s to 25 m/s.\n(a) What is the change in kinetic energy?\n(b) How much net work was done on the car?"}75{"id": 75, "title": "Work Done by Friction (Intermediate)", "question": "A 5.0 kg box slides 8.0 m across the floor, experiencing 10 N of kinetic friction.\n(a) How much work does friction do?\n(b) If the box started with a speed of 6.0 m/s, what is its final speed?"}76{"id": 76, "title": "Energy Conservation on a Hill (Rollercoaster-style)", "question": "A 0.50 kg cart is released from rest at a height of 2.0 m and rolls down a frictionless track.\n(a) What is its speed at the bottom of the hill?\n(b) If it then climbs another hill to a height of 1.0 m, what is its speed at the top?"}77{"id": 77, "title": "Work–Kinematics Combo (Advanced)", "question": "A 10.0 kg crate is pulled across a rough floor by a 50 N force at 20° above the horizontal. The\ncoefficient of kinetic friction is 0.3. The crate moves 6.0 m.\n(a) What is the work done by the pulling force?\n(b) What is the work done by friction?\n(c) Using energy conservation, find the final speed of the crate if it started from rest.\n(Requires breaking force into components, calculating normal force, using both W = F·d and\nenergy ideas.)"}78{"id": 78, "title": "Energy Recovery Problem (Creative)", "question": "A 2.0 kg object is dropped from height hhh, bounces off a spring (k = 400 N/m), and rebounds\nto 60% of its original height.\n(a) What was the original height hhh?\n(b) What is the maximum compression of the spring during the bounce?\n(Requires conservation of energy in both directions, including PE → KE → spring PE and\npartial recovery.)"}79{"id": 79, "title": "Slide and Launch (Multi-Concept)", "question": "A 1.5 kg mass slides down a frictionless ramp from 2.0 m high, then launches horizontally off\nthe edge and lands 1.8 m from the base.\n(a) What was its speed at the bottom of the ramp?\n(b) Confirm the landing distance using projectile motion.\n(Requires conservation of energy AND 2D kinematics.)"}80{"id": 80, "title": "Power and Hill Climb (Integrated Challenge)", "question": "A 1200 kg car drives up a 30° hill. The engine provides 40 kW of power. The car’s speed is\nconstant at 15 m/s.\n(a) What is the component of weight acting down the slope?\n(b) How much power is used to overcome gravity?\n(c) How much excess power (if any) is available for acceleration or other forces?"}81{"id": 81, "title": "Recoil Launch Pad (Advanced + Hidden Energy)", "question": "A 2.0 kg object is on a spring-loaded platform (k = 800 N/m). It is launched vertically. The spring\nis compressed 0.30 m before release.\n(a) What is the launch speed of the object?\n(b) What maximum height does it reach?\n(c) How long is it in the air total?\n(Requires spring energy → KE → PE, and full vertical motion analysis.)"}82{"id": 82, "title": "Variable Friction + Kinematics (Advanced)", "question": "A sled of mass 10 kg is pulled across a 20 m stretch of snow where the coefficient of kinetic\nfriction starts at 0.05 and increases linearly to 0.25.\n(a) Estimate the average frictional force over the distance.\n(b) If pulled with a constant 50 N horizontal force, what is its final speed starting from rest?\n(Requires estimating variable friction, using work–energy theorem and possibly kinematics for\nvalidation.)"}83{"id": 83, "title": "Loop-the-Loop Power Drop (Extreme Multi-Step)", "question": "A 0.5 kg object starts at the top of a frictionless ramp 5.0 m high, enters a vertical loop (radius\n1.0 m), and exits the loop at the bottom.\n(a) What is its speed at the top of the loop?\n(b) What is the normal force at the top of the loop?\n(c) How much power would be needed to drag the object up to its starting point at a constant\nspeed in 10 seconds?\n(Requires energy conservation, Newton’s 2nd Law at top of loop, and power = work/time.)\n🔥 ADVANCED WORK, ENERGY & POWER PROBLEMS 🔥\nBe prepared to think, draw free-body diagrams, and link multiple concepts."}84{"id": 84, "title": "Vertical Launch with Friction on Takeoff Track", "question": "A 3.0 kg projectile is launched vertically by sliding along a 2.5 m frictional track that inclines at\n60°. The coefficient of kinetic friction is 0.30, and the projectile compresses a spring (k = 1200\nN/m) by 0.40 m before release.\n(a) What is the net work done on the object by the spring?\n(b) How much energy is lost to friction during the launch?\n(c) What is the object’s speed at the top of the ramp?\n(d) How high does the object rise above the launch point after leaving the ramp?\n(Spring work, friction loss, kinematics + projectile vertical motion.)"}85{"id": 85, "title": "Power-Limited Car with a Climb & Acceleration", "question": "A 1500 kg car starts from rest and climbs a 10° incline that is 150 m long. The car engine\nprovides a constant power output of 40 kW.\n(a) What is the total energy required to reach the top at constant speed?\n(b) If instead the car accelerates uniformly and reaches the top in 12 seconds, what is its final\nspeed?\n(c) Was the engine capable of doing this in time? Justify with power calculations.\n(Power = work/time, energy = KE + PE, test if actual required power ≤ 40 kW.)"}86{"id": 86, "title": "Spring Launch to Vertical Loop with Friction", "question": "A small block of mass 1.0 kg is launched by a spring (k = 1000 N/m) that is compressed 0.3 m.\nThe block travels along a track and goes through a vertical loop of radius 0.75 m. The track\nhas a total of 2.0 m of rough surface before the loop, with μk=0.25\\mu_k = 0.25μk =0.25.\n(a) What is the speed just before entering the loop?\n(b) What is the minimum speed at the top of the loop to maintain contact?\n(c) Does the block complete the loop? Prove it.\n(Involves spring PE, frictional work loss, KE, and circular motion.)"}87{"id": 87, "title": "Rocket Sled with Phase-Based Acceleration", "question": "A sled of mass 400 kg is pushed across a level track. For the first 50 m, it is powered by a\nrocket producing 2000 N of thrust. After the rocket cuts off, it coasts another 100 m against a\nkinetic friction force of 500 N before stopping.\n(a) What is the sled’s speed at the end of the powered phase?\n(b) Use energy conservation to find how far it would travel if there were no friction.\n(c) What is the total work done by friction in the second phase?\n(Two-phase motion: forced + coast. Work-energy for both.)"}88{"id": 88, "title": "Mass Pulled Up and Released from Spring Track", "question": "A block of mass 2.0 kg is pulled up a frictionless ramp inclined at 40°, attached to a spring with\nk = 250 N/m at the top. The block is pulled so that it compresses the spring 0.5 m and held in\nplace.\n(a) When released, what is the block’s speed when it passes the point where the spring is\nuncompressed?\n(b) How far up the ramp does the block rise beyond that point before turning around (while still\non the ramp)?\n(c) How much time does it take to go from the release point to the moment it stops moving up\nthe ramp?\n(Spring energy → KE → PE. Requires energy AND kinematics.)"}89{"id": 89, "title": "Energy Hunt in a Swinging Rope", "question": "A student swings on a rope (length 5.0 m) from rest at an angle of 30° with the vertical.\n(a) What is their speed at the lowest point?\n(b) What is the tension in the rope at that point, assuming mass = 60 kg?\n(c) If they let go at that lowest point, how far horizontally will they land?\n(Requires PE → KE, then force analysis at the bottom, then projectile motion.)"}90{"id": 90, "title": "Dropping Onto a Spring on a Platform (Energy & Kinematics)", "question": "A 4.0 kg block is dropped from a height of 3.0 m onto a vertical spring with spring constant 600\nN/m. The spring is mounted on a 2.0 kg platform, which rests on a frictionless surface and is\nfree to move.\n(a) What is the maximum compression of the spring?\n(b) What is the speed of the platform at that moment?\n(c) What energy transfer causes the platform to move?\n(Requires full system momentum + energy conservation, and center-of-mass motion analysis\n⚡ MOMENTUM & IMPULSE PROBLEMS (With Energy)\nProgressively harder, multi-concept. Kinematics appears where needed. All realistic."}91{"id": 91, "title": "Basic Impulse", "question": "A 0.15 kg baseball is pitched at 40 m/s and hit back in the opposite direction at 50 m/s.\n(a) What is the impulse delivered to the ball?\n(b) If the bat is in contact with the ball for 0.005 s, what average force does it exert?"}92{"id": 92, "title": "Simple Inelastic Collision", "question": "A 2.0 kg cart moving at 3.0 m/s collides and sticks to a 1.0 kg cart at rest.\n(a) What is the final velocity of the combined mass?\n(b) How much kinetic energy is lost during the collision?"}93{"id": 93, "title": "Bouncing vs Sticking", "question": "A 0.5 kg ball hits a wall at 10 m/s and rebounds straight back at 8 m/s.\n(a) What is the impulse on the ball?\n(b) If a second identical ball hits the wall and sticks instead, what’s the difference in impulse?\n(c) Which collision transfers more momentum to the wall?"}94{"id": 94, "title": "Collision on a Track with Friction Aftermath", "question": "A 3.0 kg cart moving at 2.5 m/s collides with and sticks to a 2.0 kg cart at rest. After the\ncollision, the combined carts slide 1.2 m before stopping due to friction.\n(a) What is the coefficient of kinetic friction?\n(b) How much energy was lost in the collision?"}95{"id": 95, "title": "Bullet into Block – Hanging Pendulum", "question": "A 10 g bullet traveling at 500 m/s embeds itself in a 2.0 kg wooden block hanging from a string.\nThe block swings upward.\n(a) What is the speed of the block+bullet immediately after the collision?\n(b) How high does the block rise?\n(c) How much mechanical energy is lost?"}96{"id": 96, "title": "Ramp Collision Escape (Momentum + Energy)", "question": "A 1.0 kg cart moving at 4.0 m/s hits a stationary 1.5 kg cart at the bottom of a frictionless ramp.\nAfter the perfectly elastic collision, the 1.5 kg cart rolls up the ramp.\n(a) What are the final velocities of both carts after the collision?\n(b) How high does the 1.5 kg cart rise on the ramp?"}97{"id": 97, "title": "Two-Dimensional Explosion (Momentum + Energy)", "question": "A firecracker explodes into three pieces of equal mass. One piece travels at 5.0 m/s due east,\nthe second at 6.0 m/s due north.\n(a) Find the speed and direction of the third piece.\n(b) Was kinetic energy conserved? Explain why or why not."}98{"id": 98, "title": "Ballistic Pendulum with a Twist", "question": "A 50 g steel ball is fired into a hanging block (mass = 1.5 kg) attached to a spring (k = 300\nN/m). The block recoils and compresses the spring 0.10 m.\n(a) What is the speed of the block+ball after the collision?\n(b) What was the speed of the ball before impact?\n(c) How much energy is lost?"}99{"id": 99, "title": "Recoil and Friction Track (Multi-phase)", "question": "A 0.4 kg projectile is launched horizontally from a 3.6 kg cart at 20 m/s. The cart recoils and\nslides 1.5 m on a horizontal surface with μ = 0.1.\n(a) What is the recoil speed of the cart?\n(b) What is the initial kinetic energy of the cart?\n(c) Use energy ideas to confirm how far it travels before stopping."}100{"id": 100, "title": "“Jump and Slide” Collision Challenge", "question": "A student jumps from a 1.0 m high platform onto a 20 kg stationary skateboard. Their mass is\n60 kg, and they land perfectly vertically.\n(a) What is the student’s speed just before landing?\n(b) Use conservation of momentum to find the final speed of the student+skateboard.\n(c) How far do they roll before stopping if the coefficient of kinetic friction is 0.15?"}101{"id": 101, "title": "Elastic Head-On, Then Ramp Climb", "question": "A 2.0 kg cart moving at 3.0 m/s collides elastically with a 1.0 kg cart at rest. The 1.0 kg cart\nthen goes up a 20° incline.\n(a) What is the final speed of the 1.0 kg cart?\n(b) How far up the ramp does it go before turning around?\n(c) Prove energy was conserved after the collision."}102{"id": 102, "title": "Explosion on Ice (Multi-object Momentum Conservation)", "question": "Three students (mass = 50 kg each) sit on a frictionless frozen lake. One throws a 2.0 kg\nbackpack at 6.0 m/s to the right.\n(a) What is the recoil speed of the student who threw it?\n(b) If another catches it while at rest, what is their speed after?\n(c) What is the total kinetic energy of the system before and after the throw?\n💣 HIGH-CONCEPT MOMENTUM + ENERGY PROBLEMS"}103{"id": 103, "title": "The Ultimate Ballistic Pendulum", "question": "A 0.010 kg bullet is fired at 600 m/s into a 1.5 kg block hanging from a 1.0 m long light string.\nThe bullet embeds in the block.\nAfter swinging upward, the block compresses a spring at the top of its arc by 3.5 cm (spring\nconstant k = 200 N/m).\n(a) What is the speed of the block+bullet immediately after the collision?\n(b) What height did the system rise to before hitting the spring?\n(c) Confirm total energy conservation from post-collision to max spring compression.\n(d) What percentage of the original energy was lost during the collision?"}104{"id": 104, "title": "Oblique Collision with Rotation Ignored", "question": "A 2.0 kg puck traveling at 3.0 m/s on frictionless ice strikes a stationary 1.0 kg puck at a\nglancing angle, imparting a speed of 2.5 m/s at 60° to its original path.\nAssuming a perfectly elastic collision:\n(a) What are the x and y components of momentum before and after?\n(b) What is the velocity (magnitude and angle) of the second puck?\n(c) Show that kinetic energy is conserved."}105{"id": 105, "title": "Elastic Ramp Launch", "question": "A 0.50 kg block slides at 4.0 m/s on a frictionless horizontal table into a massless spring (k =\n800 N/m). After compressing it, the block is launched up a 35° incline with μ = 0.15.\n(a) What is the maximum compression of the spring?\n(b) How far up the incline does the block travel before coming to rest?\n(c) How much mechanical energy is lost to friction?"}106{"id": 106, "title": "Recoil + Drag Energy System", "question": "A 3.0 kg cannon (on a flat frictionless track) fires a 0.1 kg projectile horizontally at 120 m/s.\nThe cannon recoils and then enters a patch of kinetic friction (μ = 0.2) lasting 5.0 m.\n(a) What is the recoil velocity of the cannon immediately after firing?\n(b) How far into the friction zone does it travel before stopping?\n(c) What is the thermal energy dissipated?"}107{"id": 107, "title": "Explosion on a Hill with Projectile Outcome", "question": "A stationary 3-part probe (total mass = 6.0 kg) sitting on a snowy hill explodes into three 2.0\nkg pieces.\nOne piece slides up the hill at 4.0 m/s, another down the hill at 6.0 m/s.\nThe hill angle is 20°, and there's negligible friction.\n(a) What is the velocity (magnitude and angle) of the third piece immediately after explosion?\n(b) If it leaves the hill as a projectile, how far horizontally does it land below the explosion\npoint?"}108{"id": 108, "title": "The Sliding Collision Pendulum Drop", "question": "A 1.5 kg block slides at 5.0 m/s across a frictionless table and hits a 2.0 kg hanging block\nconnected via an inextensible rope over a pulley. The rope then goes taut and the hanging mass\nis pulled upward while the sliding block slows.\nAssume the rope goes slackless and the pulley is frictionless and massless.\n(a) What is the speed of each block immediately after the string becomes taut (inelastic\nconnection)?\n(b) How much energy is lost in this process?\n(c) How high does the hanging mass rise?"}109{"id": 109, "title": "The Smart Wall Bounce", "question": "A 0.3 kg ball is thrown at 15 m/s at a 30° angle toward a perfectly rigid wall, bounces\nelastically, and continues to hit a second block of mass 0.5 kg at rest 2.0 m away.\n(a) What is the ball's velocity vector after the wall bounce?\n(b) If the collision is elastic and head-on, what is the speed of the block afterward?\n(c) Prove energy and x-momentum are conserved (explain y-component cancellation due to\nwall interaction)."}110{"id": 110, "title": "Exploding Rod (Conceptual + Quantitative)", "question": "A light rod of length 4.0 m and mass 8.0 kg lies at rest on ice. It explodes in the center,\nbreaking into two 4.0 kg pieces.\nThe left half slides west at 6.0 m/s.\n(a) What is the velocity of the right half?\n(b) How far is the center of mass from the original position after 3.0 s?\n(c) Is mechanical energy conserved? Justify using total kinetic energy before and after."}111{"id": 111, "title": "Drop-Catch Energy-Momentum Mix", "question": "A 1.0 kg ball is dropped from 2.0 m and bounces perfectly elastically off a 3.0 kg cart that is\ninitially at rest on a frictionless surface.\n(a) What is the ball's speed just before impact?\n(b) After bouncing, the ball rises to 1.6 m. What is its new speed?\n(c) What is the final velocity of the cart?\n(d) Verify total momentum is conserved, but not total mechanical energy of the cart+ball\nsystem."}112{"id": 112, "title": "Rocket Booster Recoil on Ice (Continuous Mass Loss)", "question": "A 20 kg sled rests on a frictionless lake. It begins firing a small stream of 0.2 kg/s of sand out\nthe back at 10 m/s relative to the sled for 10 seconds.\n(a) What is the total impulse delivered to the sled?\n(b) What is its final speed?\n(c) How much kinetic energy does the sled gain, and how much energy was carried away by\nthe sand?\n⚙ ROTATION, TORQUE, ANGULAR MOMENTUM & ENERGY PROBLEMS\n(Progressively more complex. Includes pure rotation and translation-rotation hybrids.)"}113{"id": 113, "title": "Basic Rotation and Inertia", "question": "A solid disk (mass = 2.0 kg, radius = 0.30 m) spins about its center at 10 rad/s.\n(a) What is its rotational kinetic energy?\n(b) What is its angular momentum?"}114{"id": 114, "title": "Torque and Angular Acceleration", "question": "A 5.0 N force is applied tangentially to the edge of a wheel (I = 0.8 kg·m², r = 0.4 m).\n(a) What torque is produced?\n(b) What is the angular acceleration of the wheel?"}115{"id": 115, "title": "Falling Rod Pivoted at One End", "question": "A uniform rod of mass 4.0 kg and length 1.5 m is held horizontally and then released from rest\nto rotate about a fixed end.\n(a) What is its angular speed just before it reaches vertical?\n(b) What is the linear speed of the free end at that moment?\n(c) How much rotational kinetic energy does it have?"}116{"id": 116, "title": "Yo-Yo Drop (Rotation + Translation)", "question": "A yo-yo (mass = 0.25 kg, I = 0.0025 kg·m², radius = 0.03 m) is released from rest and unwinds\nas it falls.\n(a) What is its acceleration as it descends?\n(b) What is the tension in the string?\n(c) How fast is it spinning after falling 1.2 m?"}117{"id": 117, "title": "Rolling Without Slipping (Mixed Dynamics)", "question": "A solid cylinder of mass 2.0 kg and radius 0.10 m rolls without slipping down a 1.2 m high\nramp.\n(a) What is its speed at the bottom?\n(b) What fraction of its total energy is rotational?\n(c) What would change if it were a hollow cylinder?"}118{"id": 118, "title": "Pulley-Mass System", "question": "A block of mass 1.5 kg hangs from a string wrapped around a pulley (I = 0.04 kg·m², radius =\n0.10 m). The pulley rotates as the block falls.\n(a) Find the acceleration of the falling block.\n(b) What is the tension in the string?\n(c) How much angular velocity does the pulley gain after 2.0 m of descent?"}119{"id": 119, "title": "Angular Momentum Conservation – Collapsing Star", "question": "A rotating star has an initial moment of inertia I1=1.0×1038 kg\\cdotpm2I_1 = 1.0 \\times 10^{38}\n\\, \\text{kg·m}^2I1 =1.0×1038kg\\cdotpm2 and rotates at 1.0 revolution per day. It collapses into a\nneutron star with moment of inertia I2=1.0×1031 kg\\cdotpm2I_2 = 1.0 \\times 10^{31} \\,\n\\text{kg·m}^2I2 =1.0×1031kg\\cdotpm2.\n(a) What is its final angular velocity in rad/s?\n(b) What happens to its rotational kinetic energy?"}120{"id": 120, "title": "Twirling Skater (Classic Angular Momentum)", "question": "A 50 kg skater spins with arms extended (I = 4.0 kg·m²) at 2.0 rad/s. She pulls in her arms,\nreducing her moment of inertia to 1.5 kg·m².\n(a) What is her new angular velocity?\n(b) What is her final rotational kinetic energy?\n(c) Where did the extra energy come from?"}121{"id": 121, "title": "Rotational Collision (Rod + Point Mass)", "question": "A uniform thin rod (mass = 3.0 kg, length = 1.2 m) is pivoted at one end and initially at rest. A\n0.50 kg ball moving horizontally at 6.0 m/s strikes and sticks to the free end.\n(a) What is the angular momentum of the ball before impact?\n(b) What is the angular velocity of the rod + ball right after the collision?\n(c) How much energy was lost during the collision?"}122{"id": 122, "title": "Disk Hit by Falling Mass (Rotation + Energy)", "question": "A 2.0 kg mass is dropped from 0.75 m onto a stationary horizontal disk (I = 0.6 kg·m², radius =\n0.4 m). The mass lands 0.3 m from the center and sticks, causing the disk to spin.\n(a) What is the angular speed of the system after the impact?\n(b) Compare the mechanical energy before and after.\n(c) Identify the sources of energy loss."}123{"id": 123, "title": "Bar and Bullet Collision (Advanced)", "question": "A thin rod (mass = 2.0 kg, length = 0.8 m) pivots about its center. A 0.05 kg bullet traveling at\n300 m/s strikes the end of the rod and embeds.\n(a) What is the angular momentum of the bullet?\n(b) What is the angular velocity of the system after the impact?\n(c) How much rotational kinetic energy does it have?"}124{"id": 124, "title": "Rotating Platform Catch (Multi-Stage)", "question": "A student sits on a rotating stool holding a 2.0 kg medicine ball spinning at 1.2 rad/s (system I =\n5.0 kg·m²). She catches a 1.0 kg ball thrown toward her at 3.0 m/s from 1.5 m away (relative to\ncenter).\n(a) What is the system’s angular velocity after she catches the ball?\n(b) What is the change in rotational kinetic energy?\n(c) Explain what caused this change."}125{"id": 125, "title": "Tilted Rod on Pivoted Table (Final Boss)", "question": "A uniform rod of length 1.0 m and mass 3.0 kg lies on a pivoted table, free to rotate in the\nhorizontal plane. A 0.25 kg ball traveling at 10 m/s hits the rod 0.75 m from the pivot and\nbounces back at 2.0 m/s.\n(a) What is the net angular momentum transferred to the rod?\n(b) What is the angular velocity of the rod after the collision?\n(c) What percentage of the ball’s energy is transferred into rotational motion?\n🔁 ROTATIONAL MOTION & TORQUE – MID-TIER PROBLEMS (AP Physics\nC Style)"}126{"id": 126, "title": "Torque on a Ladder", "question": "A uniform ladder of length 4.0 m and mass 20 kg rests against a smooth vertical wall. The\nground is rough, and the ladder makes a 60° angle with the ground.\n(a) Draw and label all forces acting on the ladder.\n(b) Find the minimum coefficient of static friction needed to prevent slipping."}127{"id": 127, "title": "Rotating Rod from Pivot", "question": "A uniform rod of mass 3.0 kg and length 1.2 m is pivoted at one end and released from rest\nhorizontally.\n(a) What is the angular acceleration at the moment of release?\n(b) What is the angular speed when it passes through vertical?\n(c) What is the linear speed of the tip at that point?"}128{"id": 128, "title": "Disk Pulled by a String (Rolling Condition)", "question": "A solid disk (mass = 2.5 kg, radius = 0.15 m) rests on a horizontal surface. A string is wrapped\naround the disk and pulled horizontally with a force of 6.0 N. The disk rolls without slipping.\n(a) Find the linear acceleration of the center of mass.\n(b) Find the friction force acting on the disk.\n(c) What is the angular acceleration?"}129{"id": 129, "title": "Cylinder Down a Ramp (Energy + Rolling)", "question": "A solid cylinder of mass 1.5 kg and radius 0.2 m rolls without slipping down a 2.0 m high ramp\ninclined at 25°.\n(a) What is its speed at the bottom?\n(b) How much of its total energy is rotational?\n(c) How would your answer change if it were a hollow cylinder?"}130{"id": 130, "title": "Rotational Work-Energy Theorem", "question": "A constant torque of 4.0 N·m is applied to a wheel (I = 0.5 kg·m²), initially at rest.\n(a) What is the angular velocity after 3.0 s?\n(b) How much work was done on the wheel?\n(c) What is the final rotational kinetic energy?"}131{"id": 131, "title": "Angular Momentum of a Rotating Platform", "question": "A 3.0 kg child stands 1.2 m from the center of a platform rotating at 1.5 rad/s. The platform has\na moment of inertia of 150 kg·m².\n(a) What is the total angular momentum of the system?\n(b) If the child walks inward to 0.6 m, what is the new angular speed of the platform?"}132{"id": 132, "title": "Suspended Pulley + Falling Mass", "question": "A pulley (mass = 2.0 kg, radius = 0.20 m, I = ½MR²) has a rope wrapped around it. A 1.5 kg\nmass hangs from the rope and is released.\n(a) Find the angular acceleration of the pulley.\n(b) What is the acceleration of the falling mass?\n(c) What is the tension in the rope?"}133{"id": 133, "title": "Two Rotating Disks (Inelastic Angular Collision)", "question": "Disk A (I = 0.4 kg·m²) spins at 6.0 rad/s. Disk B (I = 0.6 kg·m²) is at rest. They are brought into\ncontact via a clutch and rotate together.\n(a) What is their final angular velocity?\n(b) How much kinetic energy was lost in the process?\n(c) What principle justifies the method used?"}134{"id": 134, "title": "Turntable Drop Catch", "question": "A small object (0.5 kg) is dropped onto a spinning turntable (I = 0.2 kg·m², ω = 5.0 rad/s) at a\nradius of 0.2 m. The object sticks.\n(a) What is the new angular velocity of the system?\n(b) What is the change in rotational kinetic energy?\n(c) Where did the energy go?"}135{"id": 135, "title": "Force Applied Off-Center (Torque from Geometry)", "question": "A force of 10 N is applied at a point 0.3 m from the axis of rotation, at an angle of 45° to the\nradius.\n(a) What is the torque?\n(b) If this torque is applied to a disk with I = 0.6 kg·m², what is the angular acceleration?"}136