The irregular object is dropped from rest on the moon, where there is no air. Its center of mass is as shown in the figure. What will it do after it is dropped?
A. It will start rotating clockwise about its center of mass.
B. It will start rotating counterclockwise about its center of mass.
C. It will rotate until point $A$ is directly below its center of mass, and then it will stop turning.
D. It will rotate until point $A$ is directly above its center of mass, and then it will stop turning.
E. It will not rotate.

Suppose you increase the amplitude of oscillation of a mass vibrating on a spring. Which of the following statements about this mass are correct?
A. Its maximum speed increases.
B. Its period of oscillation increases.
C. Its maximum acceleration increases.
D. Its maximum kinetic energy increases.

A bicycle wheel rotating at a rate of $12 \mathrm{rad} / \mathrm{s}$ begins to accelerate at a rate of $2 \mathrm{rad} / \mathrm{s}^2$. After 5 seconds the rate of rotation will be
A. $2 \mathrm{rad} / \mathrm{s}$
B. $10 \mathrm{rad} / \mathrm{s}$
C. $17 \mathrm{rad} / \mathrm{s}$
D. $22 \mathrm{rad} / \mathrm{s}$

A thin uniform rod of mass $M$ and length $L$ is bent at its center so that the two segments are now perpendicular to each other. Find its moment of inertia about an axis perpendicular to its plane and passing through
(b) the midpoint of the line connecting its two ends.

A student rotates on a frictionless piano stool with his arms outstretched, a heavy weight in each hand. Suddenly he lets go of the weights, and they fall to the floor. As a result, does the student's angular speed increase, decrease, or stay the same? Explain.

Two points are on a disk that rotates about an axis perpendicular to the plane of the disk at its center. Point $B$ is 3 times as far from the axis as point $A$. If the linear speed of point $B$ is $V$, then the linear speed of point $A$ is
A. $9 \mathrm{~V}$
B. $3 \mathrm{~V}$
C. V
D. $\frac{V}{3}$.
E. $\frac{V}{9}$.

A uniform beam is suspended horizontally and attached to a wall by a small hinge . What are the directions (upward or downward, and to the left or the right) of the components of the force that the hinge exerts on the beam? Explain.

A uniform beam is suspended horizontally. It is attached to the wall by a small hinge. The force that the hinge exerts on the beam has components
A. upward and to the right.
B. upward and to the left.
C. downward and to the right.
D. downward and to the.

A uniform ball rolls without slipping toward a hill with a forward speed $V$. In which case will this ball go farther up the hill?
A. There is enough friction on the hill to prevent slipping of the ball.
B. The hill is frictionless.
C. The ball will reach the same height in both cases, since it has the same initial kinetic energy in each case.

When a wheel turns through one complete rotation, the angle (in radians) that it has turned through is closest to
A. $57$
B. $6$
C. $360$ .

Two identical merry-go-rounds are rotating at the same speed. One is crowded with riding children; the other is nearly empty. If both merry-go-rounds cut off their motors at the same time and coast to a stop, slowed only by friction (which you can assume is the same for both merry-go-rounds), which will take longer to stop?
A. The crowded merry-go-round
B. The empty merry-go-round
C. The same time for both.

A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of

$$125 \mathrm { kg } \cdot \mathrm { m } ^ { 2 }$$

When one person is standing at a distance of 1.50 m from the center, the carousel has an angular velocity of 0.600 rad/s. However, as this person moves inward to a point located 0.750 m from the center, the angular velocity increases to 0.800 rad/s. What is the person's mass?

You are designing a flywheel to store large amounts of kinetic energy. Which one of the following uniform shapes will be the most effective for storing the greatest amount of kinetic energy if all the objects have the same mass and the same angular velocity?
A. A solid sphere of diameter $D$ rotating about a diameter.
B. A solid cylinder of diameter $D$ rotating about an axis perpendicular to each face through its center.
C. A thin-walled hollow cylinder of diameter $D$ rotating about an axis perpendicular to the plane of the circular face at its center.
D. A solid thin bar of length $D$ rotating about an axis perpendicular to it at its center.

Two small objects of equal weight are attached to the ends of a thin weightless bar that spins about an axis perpendicular to the bar at its center. Each mass is a distance $d$ from the axis of rotation. The system spins at a rate so that its kinetic energy is $K$. If both masses are now moved closer in so that each is $d / 2$ from the rotation axis, while the angular velocity does not change, the kinetic energy of the system will be
A. $\frac{1}{4} K$.
B. $\frac{1}{2} K$.
C. $2 K$.
D. $4 K$.