### Conceptual Questions

### 10.1 Rotational Variables

A clock is mounted on the wall. As you look at it, what is the direction of the angular velocity vector of the second hand?

What is the value of the angular acceleration of the second hand of the clock on the wall?

A baseball bat is swung. Do all points on the bat have the same angular velocity? The same tangential speed?

The blades of a blender on a counter are rotating clockwise as you look into it from the top. If the blender is put to a greater speed what direction is the angular acceleration of the blades?

### 10.2 Rotation with Constant Angular Acceleration

If a rigid body has a constant angular acceleration, what is the functional form of the angular velocity in terms of the time variable?

If a rigid body has a constant angular acceleration, what is the functional form of the angular position?

If the angular acceleration of a rigid body is zero, what is the functional form of the angular velocity?

A massless tether with a masses tied to both ends rotates about a fixed axis through the center. Can the total acceleration of the tether/mass combination be zero if the angular velocity is constant?

### 10.3 Relating Angular and Translational Quantities

Explain why centripetal acceleration changes the direction of velocity in circular motion but not its magnitude.

In circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction. Explain your answer.

Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it experience nonzero tangential acceleration, centripetal acceleration, or both when: (a) the plate starts to spin faster? (b) The plate rotates at constant angular velocity? (c) The plate slows to a halt?

### 10.4 Moment of Inertia and Rotational Kinetic Energy

What if another planet the same size as Earth were put into orbit around the Sun along with Earth. Would the moment of inertia of the system increase, decrease, or stay the same?

A solid sphere is rotating about an axis through its center at a constant rotation rate. Another hollow sphere of the same mass and radius is rotating about its axis through the center at the same rotation rate. Which sphere has a greater rotational kinetic energy?

### 10.5 Calculating Moments of Inertia

If a child walks toward the center of a merry-go-round, does the moment of inertia increase or decrease?

A discus thrower rotates with a discus in his hand before letting it go. (a) How does his moment of inertia change after releasing the discus? (b) What would be a good approximation to use in calculating the moment of inertia of the discus thrower and discus?

Does increasing the number of blades on a propeller increase or decrease its moment of inertia, and why?

The moment of inertia of a long rod spun around an axis through one end perpendicular to its length is $m{L}^{2}\text{/}3$. Why is this moment of inertia greater than it would be if you spun a point mass *m* at the location of the center of mass of the rod (at *L*/2) (that would be $m{L}^{2}\text{/}4$)?

Why is the moment of inertia of a hoop that has a mass *M* and a radius *R* greater than the moment of inertia of a disk that has the same mass and radius?

### 10.6 Torque

Give an example in which a small force exerts a large torque. Give another example in which a large force exerts a small torque.

When reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations than would an identical reduction in the mass of the bicycle’s frame?

Can a single force produce a zero torque?

Can a set of forces have a net force that is zero and a net torque that is not zero?

In the expression $\overrightarrow{r}\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}\overrightarrow{F}$ can $\left|\overrightarrow{r}\right|$ ever be less than the lever arm? Can it be equal to the lever arm?

### 10.7 Newton’s Second Law for Rotation

If you were to stop a spinning wheel with a constant force, where on the wheel would you apply the force to produce the maximum negative acceleration?

A rod is pivoted about one end. Two forces $\overrightarrow{F}\text{and}\phantom{\rule{0.2em}{0ex}}-\overrightarrow{F}$ are applied to it. Under what circumstances will the rod not rotate?