Rotation in AP Physics C: Mechanics

What happens to an initially stationary rigid body if only one unbalanced external force acts upon it?

Given a non-uniform bar of length $L$ that is in rotational equilibrium while supported at two points $A$ and $B$ with $B$ being at one end of the bar; if $A$ supports three times more force than $B$, how far from $B$ is point $A$ located along the bar?

A carpenter uses a wrench to turn a bolt; knowing the bolt requires a tightening torque that is twice the carpenter can apply alone, what effect does doubling the length of the wrench have on the required force?

In terms of forces causing rotation, what does $\Sigma \tau = 0$ imply in static equilibrium for a rigid body?

A thin rod with length L pivoted at one end has two small masses attached at its opposite end; if one mass doubles while the other becomes zero, how does this change affect the system's moment of inertia about the pivot?

A solid cylinder and a hollow cylinder with the same mass and radius are rolling down an incline without slipping; which will reach the bottom first?

How much work is done by external forces holding in place a rod length L horizontally hinged at one end when it’s raised from horizontal position through angle θ given that rod’s mass m is uniformly distributed?

If two particles, each with mass m, are attached at opposite ends of a rigid weightless rod of length L that is free to rotate in space about its center, how much force must be applied perpendicular to one particle to create an angular acceleration $\alpha$?

Which one of the following quantities is not affected by the choice of pivot point when calculating torque?

What physical quantity is obtained by integrating acceleration with respect to time?