Q: A force of $$50 N is $$applied at the end of a $$0.4 m $$wrench at an angle of $$60^{\circ} to $$the handle. What is the torque produced?

$$\tau = 0.4 \times 50 \times \sin 60$$^{\circ}$$ = 17.3 N$$·m

Q: A solid uniform cylinder of mass $$2 kg $$and radius $$0.5 m $$rotates about its central axis. What is its moment of inertia?

$$I = \frac{1}{2}mr^2$ = \frac{1}{2} \times 2 \times (0.5)^2$ = 0.25 kg$$·m$$^2$$

Q: Which of the following is a condition for static equilibrium?

$$\sum F = 0$$ and $$\sum \tau = 0$$

Q: A ball of mass $$0.2 kg $$moving at $$5 m/s $$hits a wall and rebounds with $$-3 m/s. $$What is the impulse delivered to the ball?

$$J = m(v_f - v_i) = 0.2 \times (-3 - 5) = -1.6 kg$$·m/s

Q: A uniform rod of length $$2 m $$and mass $$3 kg $$rotates about its end. What is its moment of inertia?

$$I = \frac{1}{3}ml^2$ = \frac{1}{3} \times 3 \times (2)^2$ = 4 kg$$·m$$^2$$

Question 1

Which of the following best defines a radian?

Accepted Answer

The angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.

Question 2

Convert $$150^{\circ} to $$radians.

Accepted Answer

$$\frac{5\pi}{6}$$ radians

Question 3

A rotating wheel completes 10 revolutions in 5 seconds. What is its average angular velocity in rad/s?

Accepted Answer

$$4\pi$$ rad/s

Question 4

The arc length $$x of a $$circle is related to the radius $$r$$ and the angle $$	heta (in $$radians) by which equation?

Accepted Answer

$$x = r	heta$$

Question 5

A CD spins at a constant angular velocity of $$30$$ rad/s. If the radius of the CD is $$0.06 m$$, what is the linear velocity at the edge?

Accepted Answer

$$1.8 m/s$$

Question 6

A washing machine drum slows from $$600$$ rev/min to rest in $$10$$ seconds. What is its angular acceleration in rad/s$$^2$$? (1 rev = $$2\pi$$ rad)

Accepted Answer

$$-6.28/10 = -0.628$$ rad/s$$^2$$

Question 7

Which of the following statements about torque is correct?

Accepted Answer

Torque is maximized when the force is applied perpendicular to the lever arm.

Question 8

A force of $$50 N is $$applied at the end of a $$0.4 m $$wrench at an angle of $$60^{\circ} to $$the handle. What is the torque produced?

Accepted Answer

$$	au = 0.4 	imes 50 	imes \sin 60$$^{\circ}$$ = 17.3 N$$·m

Question 9

Which of the following best describes the moment of inertia?

Accepted Answer

It is the resistance of an object to changes in its rotational motion.

Question 10

A solid uniform cylinder of mass $$2 kg $$and radius $$0.5 m $$rotates about its central axis. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{2}mr^2$ = \frac{1}{2} 	imes 2 	imes (0.5)^2$ = 0.25 kg$$·m$$^2$$

Question 11

According to Newton’s second law for rotation, which equation is correct?

Accepted Answer

$$	au_{net} = I\alpha$$

Question 12

A diver tucks in to decrease her moment of inertia by half during a spin. If her initial angular velocity was $$2$$ rad/s, what is her angular velocity after tucking in (assuming angular momentum is conserved)?

Accepted Answer

$$4$$ rad/s

Question 13

Which of the following is a condition for static equilibrium?

Accepted Answer

$$\sum F = 0$$ and $$\sum 	au = 0$$

Question 14

A ball of mass $$0.2 kg $$moving at $$5 m/s $$hits a wall and rebounds with $$-3 m/s. $$What is the impulse delivered to the ball?

Accepted Answer

$$J = m(v_f - v_i) = 0.2 	imes (-3 - 5) = -1.6 kg$$·m/s

Question 15

Which of the following best describes an isolated system in physics?

Accepted Answer

A system where the net external force is zero and no mass is gained or lost.

Question 16

A seesaw is balanced with a $$40 kg $$child sitting $$2 m $$from the pivot on one side. Where should a $$50 kg $$child sit on the other side to balance the seesaw?

Accepted Answer

$$1.6 m $$from the pivot

Question 17

Which of the following is the correct expression for the angular momentum $$L of a $$rotating object?

Accepted Answer

$$L = I\omega$$

Question 18

A uniform rod of length $$2 m $$and mass $$3 kg $$rotates about its end. What is its moment of inertia?

Accepted Answer

$$I = \frac{1}{3}ml^2$ = \frac{1}{3} 	imes 3 	imes (2)^2$ = 4 kg$$·m$$^2$$

Question 19

A spinning ice skater pulls in her arms, reducing her moment of inertia to half its original value. What happens to her angular velocity?

Accepted Answer

It doubles.

Physics Study Guide: Rotational Motion, Torque, Moment of Inertia, and Angular Momentum

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