Q: If a car’s tires are spinning and producing smoke, what does this indicate about the motion of the tires?

The tires are slipping, so $$v_{cm} \neq R\omega.$$

Question 1

A mechanic uses a 0.30 m long wrench to loosen a bolt. If she applies a force of 200 N perpendicular to the wrench at its end, what is the magnitude of the torque produced about the bolt?

Accepted Answer

$$60 \ \mathrm{N \cdot m}$$

Question 2

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 3

A force of $$F = 150 \ \mathrm{N} is $$applied at $$r = 0.15 \ \mathrm{m}$$ from the axis of rotation at an angle of $$60^\circ$$ above the horizontal. What is the magnitude of the torque produced?

Accepted Answer

$$22.5 \ \mathrm{N \cdot m}$$

Question 4

Which force in the diagram below produces the greatest magnitude of torque about point O, assuming all forces have the same magnitude?

Accepted Answer

$$F_4$$

Question 5

A solid uniform flywheel of mass $$m = 5.2 \ \mathrm{kg}$$ and radius $$r = 1.2 \ \mathrm{m}$$ spins down from $$500 \ \mathrm{rpm} to $$rest. What is the total work done on the flywheel? (Moment of inertia $$I = 0.5MR^2$)

Accepted Answer

$$-5.1 \ \mathrm{kJ}$$

Question 6

The rotational analog of Newton’s second law is:

Accepted Answer

$$\sum 	au = I \alpha$$

Question 7

A cable drum (solid cylinder) has a mass $$M$$ and radius $$R. If a $$net torque of $$0.54 \ \mathrm{N \cdot m} is $$applied and $$I = \frac{1}{2}MR^2$, what is the angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \frac{0.54}{0.5MR^2$}$$

Question 8

A tire is rolling without slipping with velocity $$v. $$What is the velocity of a point at the top of the tire with respect to the road?

Accepted Answer

$$2v$$

Question 9

Which of the following best describes the center of mass of a homogeneous sphere?

Accepted Answer

It is located at the geometric center of the sphere.

Question 10

The position vector of the center of mass for a system of particles is given by:

Accepted Answer

$$\vec{r}_{cm} = \frac{\sum m_i \vec{r}_i}{\sum m_i}$$

Question 11

A child pushes tangentially on a playground merry-go-round, causing it to rotate. Which force is responsible for producing the torque?

Accepted Answer

The tangential force applied by the child

Question 12

A wheel of mass $$M$$ and radius $$R is $$rolling without slipping. Its total kinetic energy is:

Accepted Answer

$$K = \frac{1}{2}Mv_{cm}^2 + \frac{1}{2}I_{cm}\$$omega^2$$

Question 13

If a car’s tires are spinning and producing smoke, what does this indicate about the motion of the tires?

Accepted Answer

The tires are slipping, so $$v_{cm} 
eq R\omega.$$

Question 14

Which of the following is true for static friction in rolling without slipping?

Accepted Answer

Static friction force changes as needed up to a maximum value.

Question 15

A disk and a donut have the same mass and radius. Which statement about their centers of mass is correct?

Accepted Answer

The disk’s center of mass is at its geometric center, but the donut’s center of mass is in the empty space.

Question 16

A force of $$9.0 \ \mathrm{N} is $$applied tangentially to a wheel of radius $$0.12 \ \mathrm{m}. $$What is the torque produced?

Accepted Answer

$$1.08 \ \mathrm{N \cdot m}$$

Question 17

A solid cylinder of mass $$M$$ and radius $$R is $$rolling without slipping. If its center of mass has velocity $$v_{cm}$$, what is the angular velocity $$\omega$$?

Accepted Answer

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

Rotation of Rigid Bodies II: Torque, Work, and Rolling Motion

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