Q: Which of the following is the correct condition for mechanical equilibrium?

$$\sum \vec{F} = 0$$ and $$\sum \tau = 0$$

Question 1

Which of the following best describes the physical quantity 'torque'?

Accepted Answer

The product of force and the distance from the pivot to the point of force application, considering only the component of force perpendicular to the lever arm: $$	au = rF\sin	heta$$

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

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

Accepted Answer

2 kg

Question 4

Which of the following statements about rotational equilibrium is correct?

Accepted Answer

The sum of all external torques acting on the object must be zero: $$\sum 	au = 0$$

Question 5

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

Accepted Answer

Zero

Question 6

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

Accepted Answer

It increases because her angular speed increases

Question 7

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

Accepted Answer

$$L = I\omega$$

Question 8

A solid ball rolls without slipping down an incline. Which force is responsible for the ball’s rotational acceleration?

Accepted Answer

The force of static friction

Question 9

Which of the following best describes the right-hand rule for determining the direction of the angular velocity vector?

Accepted Answer

Curl the fingers of your right hand in the direction of rotation; your thumb points in the direction of the angular velocity vector

Question 10

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 $$2r$$ and the experiment is repeated, what happens to the angular speed?

Accepted Answer

It is halved

Question 11

Which of the following is the correct condition for mechanical equilibrium?

Accepted Answer

$$\sum \vec{F} = 0$$ and $$\sum 	au = 0$$

Question 12

A force $$\vec{F} is $$applied at an angle $$	heta to a $$lever arm $$\vec{r}. $$Which formula gives the magnitude of the torque?

Accepted Answer

$$	au = rF\sin	heta$$

Question 13

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 14

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

Accepted Answer

It results in a vector perpendicular to both $$\vec{A}$$ and $$\vec{B}$$

Question 15

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 is the change in angular momentum?

Accepted Answer

In the $$y$$ direction

Question 16

Which of the following is the correct relationship for rolling motion without slipping?

Accepted Answer

$$v_{cm} = R\omega$$

Question 17

Which of the following statements about the commutativity of rotational displacements is correct?

Accepted Answer

Large rotational displacements do not commute, but small ones do

Question 18

A force $$\vec{F} is $$exerted tangentially to a particle constrained to move in a circle of radius $$r. $$What is the resulting torque?

Accepted Answer

$$	au = rF$$

Question 19

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

Accepted Answer

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

Chapter 12: Torque and Rotational Motion – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards