Q: A rotating sculpture consists of three masses: 5.0 kg, 3.0 kg, and 2.0 kg, each attached to a light rod of length 4.0 m, rotating about its center. What is the total moment of inertia about the axis of rotation?

$$I = 5.0 \times (2.0)^2$ + 3.0 \times (0)^2$ + 2.0 \times (2.0)^2$ = 5.0 \times 4.0 + 0 + 2.0 \times 4.0 = 20.0 + 0 + 8.0 = 28.0\ \mathrm{kg\cdot m^2$}$$

Q: Which formula gives the angular momentum $$\vec{L} of a $$particle of mass $$m$$ moving with velocity $$\vec{v} at a $$position $$\vec{r}$$ from the axis?

$$\vec{L} = \vec{r} \times m \vec{v}$$

Question 1

A figure skater is spinning with her arms extended. She then pulls her arms in close to her body. What happens to her angular velocity, assuming no external torque acts on her?

Accepted Answer

Her angular velocity increases.

Question 2

Which equation correctly expresses the angular momentum $$L of a $$rigid body rotating about a fixed axis?

Accepted Answer

$$L = I \omega$$

Question 3

A diver tucks in during a somersault, reducing her moment of inertia to half its original value. If her initial angular velocity was $$\$$omega_0$$, what is her new angular velocity?

Accepted Answer

$$\omega_{new} = 2 \$$omega_0$$

Question 4

Which of the following best describes the conservation of angular momentum?

Accepted Answer

Angular momentum remains constant if no external torque acts on the system.

Question 5

A rotating sculpture consists of three masses: 5.0 kg, 3.0 kg, and 2.0 kg, each attached to a light rod of length 4.0 m, rotating about its center. What is the total moment of inertia about the axis of rotation?

Accepted Answer

$$I = 5.0 	imes (2.0)^2$ + 3.0 	imes (0)^2$ + 2.0 	imes (2.0)^2$ = 5.0 	imes 4.0 + 0 + 2.0 	imes 4.0 = 20.0 + 0 + 8.0 = 28.0\ \mathrm{kg\cdot m^2$}$$

Question 6

Which formula gives the angular momentum $$\vec{L} of a $$particle of mass $$m$$ moving with velocity $$\vec{v} at a $$position $$\vec{r}$$ from the axis?

Accepted Answer

$$\vec{L} = \vec{r} 	imes m \vec{v}$$

Question 7

A person is swirling a can around on a string and pulls the string in so the radius is halved. By what factor does the speed of the can change, assuming angular momentum is conserved?

Accepted Answer

It is doubled.

Question 8

Which physical quantity is the product of torque and angular displacement?

Accepted Answer

Work in rotational motion

Question 9

If a constant torque $$	au is $$applied to a rotating object for an angular displacement $$	heta$$, what is the work done?

Accepted Answer

$$W = 	au 	heta$$

Question 10

Which of the following statements about angular momentum is correct?

Accepted Answer

Angular momentum is a vector quantity.

Question 11

A rotating object has a moment of inertia $$I$$ and angular velocity $$\omega. If $$its moment of inertia is reduced to $$\frac{1}{3}I$$ with no external torque, what is its new angular velocity?

Accepted Answer

$$\omega_{new} = 3 \omega$$

Question 12

Which rule is used to determine the direction of angular momentum and angular velocity vectors?

Accepted Answer

Right-hand rule

Question 13

A child spins on a playground merry-go-round. If she moves closer to the center, what happens to her rotational kinetic energy, assuming no external torque?

Accepted Answer

It increases.

Question 14

Which equation represents the rotational work-energy theorem?

Accepted Answer

$$\Delta K = 	au 	heta$$

Question 15

A rotating disk has angular momentum $$L$$ and moment of inertia $$I. If $$its angular velocity is $$\omega$$, which equation is correct?

Accepted Answer

$$L = I \omega$$

Question 16

A torque $$	au is $$applied to a wheel for time $$t. $$What is the change in angular momentum $$\Delta L$$?

Accepted Answer

$$\Delta L = 	au t$$

Question 17

Which of the following is a correct expression for the power delivered in rotational motion?

Accepted Answer

$$P = 	au \omega$$

Question 18

A gymnast performing a flip tucks in to reduce her moment of inertia. What physical principle allows her to spin faster?

Accepted Answer

Conservation of angular momentum

Question 19

If a rotating object experiences no net external torque, which of the following quantities must remain constant?

Accepted Answer

Angular momentum

Angular Momentum, Work, and Power in Rotational Motion

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