Physics: Rotational Motion and Torque
Angular motion, torque, rotational inertia, and equilibrium
Physics: Rotational Motion and Torque
Angular motion, torque, rotational inertia, and equilibrium
Physics - Grade 9-12
- 1
A bicycle wheel rotates through an angular displacement of 18 radians in 3.0 seconds. Calculate the average angular velocity of the wheel.
Use the formula omega = theta divided by time.
The average angular velocity is 6.0 radians per second because angular velocity equals angular displacement divided by time, so 18 radians divided by 3.0 seconds equals 6.0 radians per second. - 2
A disk starts from rest and reaches an angular velocity of 12 radians per second in 4.0 seconds. Find its average angular acceleration.
The average angular acceleration is 3.0 radians per second squared because angular acceleration equals the change in angular velocity divided by time, so 12 radians per second divided by 4.0 seconds equals 3.0 radians per second squared. - 3
A student pushes perpendicular to a door with a force of 25 newtons at a distance of 0.80 meters from the hinge. Calculate the torque about the hinge.
For a perpendicular force, use tau = rF.
The torque is 20 newton-meters because torque equals force times lever arm distance when the force is perpendicular, so 25 newtons times 0.80 meters equals 20 newton-meters. - 4
A wrench is 0.30 meters long. A mechanic applies a force of 40 newtons at a 90 degree angle to the wrench. Calculate the torque produced.
The torque produced is 12 newton-meters because tau = rF, and 0.30 meters times 40 newtons equals 12 newton-meters. - 5
A 15 newton force is applied to a 0.50 meter wrench at an angle of 30 degrees to the wrench. Calculate the torque. Use sin 30 degrees = 0.50.
Only the perpendicular component of the force creates torque.
The torque is 3.75 newton-meters because tau = rF sin theta, so 0.50 meters times 15 newtons times 0.50 equals 3.75 newton-meters. - 6
A solid disk has a rotational inertia of 2.0 kilogram square meters. A net torque of 10 newton-meters acts on it. Calculate its angular acceleration.
The angular acceleration is 5.0 radians per second squared because net torque equals rotational inertia times angular acceleration, so alpha = 10 newton-meters divided by 2.0 kilogram square meters. - 7
A rotating object has a rotational inertia of 0.75 kilogram square meters and an angular velocity of 8.0 radians per second. Calculate its rotational kinetic energy.
Use KErot = 1/2 I omega squared.
The rotational kinetic energy is 24 joules because rotational kinetic energy equals one half I omega squared, so 0.5 times 0.75 times 8.0 squared equals 24 joules. - 8
A merry-go-round rotates at 2.0 radians per second. A child sits 1.5 meters from the center. Calculate the child's tangential speed.
The child's tangential speed is 3.0 meters per second because tangential speed equals radius times angular velocity, so 1.5 meters times 2.0 radians per second equals 3.0 meters per second. - 9
A point on a spinning wheel has a tangential speed of 6.0 meters per second. The point is 0.40 meters from the center. Calculate the angular velocity of the wheel.
Rearrange v = r omega to solve for omega.
The angular velocity is 15 radians per second because omega equals tangential speed divided by radius, so 6.0 meters per second divided by 0.40 meters equals 15 radians per second. - 10
A 2.0 meter long uniform board is supported at its center. A 30 newton weight hangs 0.60 meters to the left of the center. How far to the right of the center must a 20 newton weight be placed to balance the board?
The 20 newton weight must be placed 0.90 meters to the right of the center. For rotational equilibrium, clockwise torque equals counterclockwise torque, so 30 newtons times 0.60 meters equals 20 newtons times x, giving x = 0.90 meters. - 11
A figure skater spins with arms extended and then pulls the arms inward. Explain what happens to the skater's angular velocity and why, assuming no external torque acts.
Use conservation of angular momentum, I omega = constant.
The skater's angular velocity increases because pulling the arms inward decreases rotational inertia. With no external torque, angular momentum is conserved, so a smaller rotational inertia requires a larger angular velocity. - 12
A wheel completes 10 full rotations in 5.0 seconds. Calculate its average angular velocity in radians per second. Use 1 rotation = 2 pi radians and pi = 3.14.
First convert rotations to radians, then divide by time.
The average angular velocity is 12.56 radians per second. The wheel turns through 10 times 2 pi radians, which is 62.8 radians, and 62.8 radians divided by 5.0 seconds equals 12.56 radians per second.