Q: A wheel starts from rest and reaches an angular velocity of $$\omega_f = 2400 \text{ rpm} in$$ $$2.5 \text{ s}. $$What is the angular acceleration $$\alpha in$$ $$\text{rad/s}^2$$? (Use $$\omega_f = 251.3 \text{ rad/s})$$

$$\alpha = 100.5 \text{ rad/s}^2$$

Q: A dumbbell is balanced on a pivot. If $$m_1 = 2$$ \text{ kg}$$ at x_1$ = 1 \text{ m}$$ and $$m_2 = 3$$ \text{ kg}$$ at x_2$ = 4 \text{ m}$$, what is the x-coordinate of the center of gravity?

$$x_{cg} = \frac{m_1$ x_1$ + m_2$ x_2$}{m_1$ + m_2$} = 2.8 \text{ m}$$

Q: A flywheel (cylinder) of mass 540 kg and radius 0.30 m is spun up by a motor providing a constant torque of 2.8 N m. What is the moment of inertia of the flywheel?

$$I = \frac{1}{2} M R^2$ = 24.3 \text{ kg m}^2$$

Q: A disk rotates with constant angular acceleration. Which equation describes the angular displacement $$\Delta \theta$$ after time $$\Delta t$$?

$$\Delta \theta = \omega_i \Delta t + \frac{1}{2} \alpha (\Delta t)^2$

Q: A torque of 5 N m is applied to a wheel with a moment of inertia of 2 kg m$$^2. $$What is the angular acceleration?

$$\alpha = \frac{\tau}{I} = 2.5 \text{ rad/s}^2$$

Question 1

A child pushes a playground merry-go-round at its edge, as shown in the image. If the radius of the merry-go-round is 2 m and the child applies a force of 50 N perpendicular to the edge, what is the magnitude of the torque produced by the child?

Accepted Answer

$$	au = 100 	ext{ N m}$$

Question 2

A particle moves along a circular path with radius $$r. If $$the arc length traveled is $$s$$, what is the angular position $$	heta in $$radians?

Accepted Answer

$$	heta = \frac{s}{r}$$

Question 3

A wind turbine blade is 50 m long and rotates at 10 rpm. What is the speed of the tip of the blade? (Use $$\omega = 2\pi f$$, $$v = \omega r)$$

Accepted Answer

$$v = 52 	ext{ m/s}$$

Question 4

Which of the following best describes the difference between translational and rotational motion?

Accepted Answer

Translational motion is movement along a trajectory without rotation, while rotational motion is movement about a fixed axis.

Question 5

A rigid body rotates about a fixed axis. Which statement is true regarding the angular velocity of points on the body?

Accepted Answer

All points have the same angular velocity.

Question 6

A wheel starts from rest and reaches an angular velocity of $$\omega_f = 2400 	ext{ rpm} in$$ $$2.5 	ext{ s}. $$What is the angular acceleration $$\alpha in$$ $$	ext{rad/s}^2$$? (Use $$\omega_f = 251.3 	ext{ rad/s})$$

Accepted Answer

$$\alpha = 100.5 	ext{ rad/s}^2$$

Question 7

A 3.2 kg flagpole extends from a wall at an angle of $$25^\circ$$ from the horizontal. Its center of gravity is 1.6 m from the point of attachment. What is the gravitational torque about the attachment point? (Use $$r_\perp = r \cos 	heta$$ and $$	au = -r_\perp m g)$$

Accepted Answer

$$	au = -45 	ext{ N m}$$

Question 8

If a force is applied to a wrench at an angle $$\phi to $$the moment arm $$r$$, which equation gives the torque?

Accepted Answer

$$	au = r F \sin \phi$$

Question 9

A dumbbell is balanced on a pivot. If $$m_1 = 2$$ 	ext{ kg}$$ at x_1$ = 1 	ext{ m}$$ and $$m_2 = 3$$ 	ext{ kg}$$ at x_2$ = 4 	ext{ m}$$, what is the x-coordinate of the center of gravity?

Accepted Answer

$$x_{cg} = \frac{m_1$ x_1$ + m_2$ x_2$}{m_1$ + m_2$} = 2.8 	ext{ m}$$

Question 10

A flywheel (cylinder) of mass 540 kg and radius 0.30 m is spun up by a motor providing a constant torque of 2.8 N m. What is the moment of inertia of the flywheel?

Accepted Answer

$$I = \frac{1}{2} M R^2$ = 24.3 	ext{ kg m}^2$$

Question 11

Which force applied to a door will produce the greatest torque about the hinge?

Accepted Answer

A force applied perpendicular to the door at the farthest point from the hinge.

Question 12

For a rigid body rotating about a fixed axis, what is the relationship between tangential acceleration $$a_t$$ and angular acceleration $$\alpha$$?

Accepted Answer

$$a_t = \alpha r$$

Question 13

A disk rotates with constant angular acceleration. Which equation describes the angular displacement $$\Delta 	heta$$ after time $$\Delta t$$?

Accepted Answer

$$\Delta 	heta = \omega_i \Delta t + \frac{1}{2} \alpha (\Delta t)^2$

Question 14

A torque of 5 N m is applied to a wheel with a moment of inertia of 2 kg m$$^2. $$What is the angular acceleration?

Accepted Answer

$$\alpha = \frac{	au}{I} = 2.5 	ext{ rad/s}^2$$

Question 15

If a particle moves in a circle with radius $$r$$ and angular velocity $$\omega$$, what is its linear speed?

Accepted Answer

$$v = \omega r$$

Question 16

A rotating object experiences a net torque. What is the resulting effect according to Newton’s Second Law for Rotation?

Accepted Answer

The object will have an angular acceleration $$\alpha$$ given by $$	au_{net} = I \alpha.$$

Question 17

A bicycle crank is acted on by four forces as shown. Which force does NOT exert a torque about the axle?

Accepted Answer

The force directed along the axle ($$F_{axle}).$$

Question 18

Which of the following is the correct formula for the moment of inertia of a collection of particles?

Accepted Answer

$$I = \sum m_i r_i^2$

Rotational Motion: Physics with Algebra Study Guide

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