Q: For a rigid body in equilibrium, which two conditions must be satisfied?

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

Question 1

A solid disk rotates with angular velocity $$\omega$$ and moment of inertia $$I. If no $$external torque acts on the disk, what happens to its angular momentum?

Accepted Answer

It remains constant.

Question 2

An ice skater spins with arms outstretched (large $$I$$, small $$\omega) $$and then pulls her arms in (small $$I$$, large $$\omega). $$Which principle explains the increase in angular velocity?

Accepted Answer

Conservation of angular momentum

Question 3

A block slides in a circular path on a frictionless plane. The radius is reduced to half its original value by pulling the string. If the initial speed is $$v_i$$, what is the final speed?

Accepted Answer

$$2v_i$$

Question 4

Two disks with moments of inertia $$I_A$$ and $$I_B$$ and angular velocities $$\omega_A$$ and $$\omega_B$$ are pushed together without external torque. What is the final angular velocity $$\omega_f$$?

Accepted Answer

$$\omega_f = \frac{I_A \omega_A + I_B \omega_B}{I_A + I_B}$$

Question 5

A seesaw balances two people of masses 90 kg and 60 kg at opposite ends of a 3.0 m board. Where should the pivot be placed from the heavier person?

Accepted Answer

1.8 m

Question 6

A uniform ladder of length 5.0 m and weight 180 N leans against a frictionless wall. A knight of weight 800 N stands a third of the way up. What is the minimum coefficient of static friction needed to prevent slipping?

Accepted Answer

$$\mu_s = \frac{F_{friction}}{F_{normal}}$$

Question 7

Which of the following is NOT a vector quantity in rotational dynamics?

Accepted Answer

Moment of inertia

Question 8

The right-hand rule is used to determine the direction of which rotational quantity?

Accepted Answer

Both angular momentum and angular velocity

Question 9

A gyroscope experiences a net torque. What happens to its angular momentum?

Accepted Answer

It changes in direction.

Question 10

A bowling ball rolls without slipping down an incline at angle $$\beta. $$What is the acceleration of its center of mass?

Accepted Answer

$$a_{cm} = \frac{5}{7}g \sin \beta$$

Question 11

A yo-yo consists of a solid disk of mass $$M$$ and radius $$R. $$What is the acceleration of the yo-yo as it descends?

Accepted Answer

$$a = \frac{2g}{3}$$

Question 12

A professor stands on a turntable holding dumbbells. When he pulls the dumbbells inward, what happens to his angular velocity?

Accepted Answer

It increases.

Question 13

For a rigid body in equilibrium, which two conditions must be satisfied?

Accepted Answer

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

Question 14

The torque due to gravity on a rigid body can be treated as acting at which point?

Accepted Answer

At the center of mass

Question 15

If the net external torque on a system is zero, what happens to the system's angular momentum?

Accepted Answer

It remains constant.

Question 16

A mass $$m is $$attached to a string and moves in a circle of radius $$r$$ with speed $$v. $$What is its angular momentum?

Accepted Answer

$$L = mvr$$

Question 17

A gyroscope precesses with angular velocity $$\Omega. $$Which equation describes $$\Omega$$?

Accepted Answer

$$\Omega = \frac{	au}{L}$$

Question 18

A rigid body rotates about a fixed axis. Which equation relates torque $$	au to $$angular acceleration $$\alpha$$?

Accepted Answer

$$	au = I\alpha$$

Question 19

A bowling ball rolls down a ramp without slipping. What force is responsible for its rotation?

Accepted Answer

Friction force

Question 20

Which of the following best describes the work done by a torque $$	au$$ over an angular displacement $$\Delta 	heta$$?

Accepted Answer

$$W = 	au \Delta 	heta$$

Dynamics of Rotational Motion: Conservation, Equilibrium, and Applications

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