13. Rotational Inertia & Energy

For a rotating wheel, the angular velocity is denoted by $\omega$ and the angular acceleration by $\alpha$. If a wheel is rotating clockwise and speeding up, what are the signs of $\omega$ and $\alpha$?

Two disks are rotating about the same axis. If disk A has a moment of inertia $I_A$ and angular velocity ${\omega }_A$, and disk B has a moment of inertia $I_B$ and angular velocity ${\omega }_B$, what is the total angular momentum of the system about the axis?

When a rigid object rotates about a fixed axis, which of the following statements is true about all points on the object?

While the line of children is rotating about an axis, which of the following statements is correct?

A fan blade rotates with an angular velocity given by $\omega (t)=\alpha -\beta t^2$, where $\alpha$ and $\beta$ are positive constants. What is the angular displacement $\theta$ as a function of time if $\theta (0)=0$?

Two blocks of masses m₁ and m₂ (m₁ > m₂) are both attached to a long, light rope that is wrapped several times around a pulley, as shown below. The pulley has mass M and radius R, can be modeled as a solid cylinder, and is free to rotate about a fixed, frictionless axis perpendicular to itself and through its center. When the block is released from rest, it begins to fall, causing the pulley to unwind without slipping. Derive an expression for the angular acceleration of the pulley.

When you release a simple 100-g yo-yo from rest, it falls and rolls, unwinding the light string around its cylindrical shaft, which is 2 cm in radius. If the yo-yo can be modeled after a solid disc, calculate its linear acceleration.

A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, similar to what is shown in Fig. 10.10. The pulley is a uniform disk with mass 10.0 kg and radius 30.0 cm and turns on frictionless bearings. You measure that the stone travels 12.6 m in the first 3.00 s starting from rest. Find the mass of the stone.