Question 1

Which of the following best describes the physical meaning of torque?

Accepted Answer

The tendency of a force to cause rotational motion about an axis.

Question 2

A mechanic uses a wrench to loosen a bolt. Which arrangement will produce the greatest torque?

Accepted Answer

Applying the force at the end of the wrench, perpendicular to the wrench.

Question 3

The mathematical expression for torque when a force $$\vec{F} is $$applied at a distance $$r$$ from the pivot at an angle $$	heta is$$:

Accepted Answer

$$	au = rF\sin	heta$$

Question 4

A uniform 1-m stick is balanced at the 0.25-m mark with a 1-kg mass hanging from one end. What is the mass of the stick?

Accepted Answer

0.5 kg

Question 5

Which of the following is a condition for rotational equilibrium?

Accepted Answer

The sum of all external torques is zero.

Question 6

A wheel rolls without slipping along a horizontal surface with center speed $$v. $$What is the velocity of the lowest point on the wheel relative to the ground?

Accepted Answer

Zero

Question 7

A figure skater spins with arms extended and then pulls them in. What happens to her angular velocity and rotational kinetic energy?

Accepted Answer

Angular velocity increases; kinetic energy increases.

Question 8

Which of the following statements about the center of mass of a freely rotating object is correct?

Accepted Answer

It moves as if all the mass were concentrated at that point and all external forces were applied there.

Question 9

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

Accepted Answer

Angular velocity

Question 10

A solid ball rolls without slipping down a ramp inclined at $$30^\circ. $$Which force is responsible for both the rotational acceleration and reducing the translational acceleration compared to sliding?

Accepted Answer

Static friction

Question 11

Which of the following is true about the vector product (cross product) of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

Its direction is perpendicular to both $$\vec{A}$$ and $$\vec{B}.$$

Question 12

A puck of mass $$m$$ moving at speed $$v$$ hits an identical puck attached to a string of length $$r$$ and causes it to revolve around a pole. If the string is lengthened to $$2r$$, what happens to the angular speed?

Accepted Answer

It is halved.

Question 13

Which of the following best describes mechanical equilibrium?

Accepted Answer

Both the sum of all external forces and the sum of all external torques are zero.

Question 14

A motor exerts a constant tangential force $$F on $$the rim of a flywheel of radius $$R$$ for a time $$t. $$What is the work done by the motor?

Accepted Answer

$$W = 	au \cdot 	heta$$

Question 15

Two cylinders of equal mass and radius roll down an incline. Cylinder A has mass concentrated at the rim, Cylinder B at the center. Which reaches the bottom first?

Accepted Answer

Cylinder B

Question 16

Which of the following is the correct expression for the total kinetic energy of a rolling object?

Accepted Answer

$$K = \frac{1}{2}mv_{cm}^2 + \frac{1}{2}I\$$omega^2$$

Question 17

If the net external torque on a system is zero, what can be said about the system's angular momentum?

Accepted Answer

It remains constant.

Question 18

A person spins a tennis ball on a string in a horizontal circle and gives it a sharp blow in the forward direction. In which direction does the change in angular momentum point?

Accepted Answer

x direction

Question 19

Which of the following statements about rotational displacements is correct?

Accepted Answer

Small rotational displacements commute, but large ones do not.

Chapter 12: Torque and Rotational Dynamics – Study Notes

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