A uniform rod of length $L$ and mass $m$ is pivoted at one end and held horizontally. What is the magnitude of the gravitational torque about the pivot point due to the weight of the rod?

A 1,000 kg disc that has a 5 m outer radius is mounted on a vertical, inner axle 80 kg in mass and 1 m in radius. A motor acts on the axle to speed up or slow down the system. Suppose the motor stops functioning when the system is spinning at 70 rad/s. To bring it to a complete stop, you apply a constant 200 N friction to the surface of the axle. How many revolutions will the system take to stop?

(Note there are two objects (two I’s) and that the larger disc is NOT a solid cylinder)

A playground merry-go-round has radius $2.40\text{ m}$ and moment of inertia $2100{\text{ kg m}}^2$ about a vertical axle through its center, and it turns with negligible friction. A child applies an $18.0\text{ N}$ force tangentially to the edge of the merry-go-round for $15.0\text{ s}$. If the merry-go-round is initially at rest, what is its angular speed after this $15.0\text{ s}$ interval?

A machine part has the shape of a solid uniform sphere of mass 225 g and diameter 3.00 cm. It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 N at that point. How long will it take to decrease its rotational speed by 22.5 rad/s?

In the context of rotational motion, which factor does the torque $\tau$ on an object not depend on?

A uniform rod of length $L$ and mass $m$ is pivoted at one end and held horizontally in equilibrium by a pin at the pivot. What is the magnitude of the torque that the pin must exert to keep the rod from rotating?

A uniform pole of length $L$ and mass $m$ is pivoted at one end and held horizontally. What is the magnitude of the torque $\tau$ about the pivot due to gravity?

When applying a force to open a door, at which angle relative to the door surface is the $\tau$ (torque) produced by the force maximized?

In a rigid body rotating about a fixed axis, if segment CD is located at a distance $r$ from the axis and is subjected to a force $F$ perpendicular to the segment, what is the internal torque in segment CD?