Rotational Motion

As shown in Figure, a wheel with radius $r$ rolls without slipping on the outer surface of a fixed cylinder with radius $R$. The center of the wheel, O, moves with a constant speed $V$.

The angular velocity of a flywheel uniformly decreases from 900 rev/min to 800 rev/min in 5 seconds.

A rigid ring with radius $R$ undergoes pure rolling on a rigid horizontal surface. The center of the ring moves forward horizontally with a constant velocity $v_0$. Consider a point P on the ring that is at the same height as the center.

Calculate the angular velocities of the Earth's daily rotation about its axis and its annual revolution about the Sun.

A rigid body undergoes uniformly accelerated rotation about a fixed axis. The angular acceleration is $\alpha = 2.0 \text{ rad/s}^2$, and the initial angular velocity at $t=0$ is $\omega_0 = 4 \text{ rad/s}$.

A flywheel with a rotational speed of 1500 r/s decelerates uniformly after braking and comes to a stop in 5.0 s. The diameter of the flywheel is 1.00 m.

A thin rod of length 80 cm has a 200 g small ball attached to each end. The balls can be treated as point masses, and the mass of the rod is negligible.