Rotating Systems: Energy & Momentum

A constant torque of 10 N⋅m is applied to a wheel, causing it to rotate through an angle of 5 radians. How much work is done by the torque?

A mechanic applies a torque to tighten a bolt. If the torque and the resulting angular displacement of the bolt are in the same direction, what happens to the energy of the bolt-wrench system?

A motor applies a torque of 20 N⋅m to a shaft, causing it to rotate. If the shaft rotates 90 degrees, how much work is done by the torque? (Remember to convert to radians.)

A rotating machine part starts from rest and accelerates due to a constant torque of 5 N⋅m. After 4 seconds, its angular speed is 10 rad/s. If the rotational inertia of the part is 1 kg⋅m², how much work did the torque do during these 4 seconds?

A torque-angle graph shows a rectangular area with a base of 2 radians and a height of 5 N⋅m. How much work is done by the torque?

A torque-angle graph has an irregular shape. To estimate the work done, you divide the area under the curve into several small rectangles. If the sum of the areas of these rectangles is 25 J, what is the approximate work done by the torque?

A torque acting on a rotating object varies with angle as $\tau = 2\theta^2 + 1$ (in N⋅m, where $\theta$ is in radians). Calculate the work done by the torque as the object rotates from $\theta = 0$ to $\theta = 2$ radians.

A rotating motor increases its rotational kinetic energy from 100 J to 150 J. How much work was done by the torque?

A solid sphere and a solid disk have the same mass and radius. Which has a higher rotational inertia about its center of mass?

A spinning top is slowing down due to friction, which exerts a torque opposite to its rotation. What can be said about the energy transfer in this situation?