Rotating Systems: Energy & Momentum
A constant torque of 5 Nm is applied to a wheel. If the wheel rotates through an angle of radians, what is the work done by the torque?
5 J
10 J
2.5 J
5 J
The torque acting on a rotating object varies with angular position as . What is the work done by the torque as the object rotates from to ?
A rotating wheel connected to a spring is initially at rest. As the wheel rotates, it compresses the spring, storing potential energy. If the wheel's initial kinetic energy is 200 J and the spring stores 150 J of potential energy when the wheel stops, how much energy was lost due to friction?
50 J
100 J
150 J
200 J
A disc rotates from rest due to a constant applied torque. After some time, its rotational kinetic energy is . If the applied torque is doubled, what is the rotational kinetic energy of the disc after the same amount of time?
2KE_1
4KE_1
8KE_1
A constant torque of 12 Nm is applied to a door. The force is applied 0.5 m from the hinges. If the door rotates through 90 degrees, how much work is done?
6 J
3 J
12 J
24 J
A variable torque is given by , where A is a constant. Calculate the work done as the object rotates from to .
A
2A
0
A torque vs. angular displacement graph shows a triangle with a base of 4 radians and a height of 8 Nm. What is the work done by the torque?
8 J
16 J
32 J
4 J

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A rotating object has its rotational kinetic energy increased by 50 J due to an applied torque. According to the work-energy theorem, how much work was done by the torque?
25 J
50 J
75 J
100 J
A graph of torque vs. angular displacement is a rectangle with a height of 10 Nm and a width of 2 radians. What is the work done by the torque?
5 J
10 J
20 J
30 J
A solid cylinder is rolling without slipping and experiences a torque that does 100 J of work. If the cylinder's translational kinetic energy increases by 40 J, what is the increase in its rotational kinetic energy?
40 J
50 J
60 J
100 J