Q: A wheel rotates with a constant angular acceleration $$\alpha. If $$its initial angular velocity is $$\$$omega_0$$ and it rotates through an angular displacement $$\Delta \theta$$ in time t$, which equation correctly relates these quantities?

$$\Delta \theta = \$$omega_0$$ t + \frac{1}{2} \alpha t^2$

Q: 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 where the pole is attached. What is the magnitude of the gravitational torque about the point of attachment? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$\tau = (3.2)(9.8)(1.6) \sin 25^\circ$$

Q: A seesaw is balanced with a 22 kg child sitting 1.6 m from the pivot on one side. Where should a 25 kg child sit on the other side to balance the seesaw, assuming the seesaw's mass is negligible?

At $$x = \frac{22}{25} \times 1.6\ \mathrm{m}$$ from the pivot

Q: A solid cylinder (mass $$M$$, radius $$R) is $$spun up from rest by a constant torque $$\tau. $$What is the angular acceleration $$\alpha$$?

$$\alpha = \frac{2\tau}{M R^2$}$$

Q: A flywheel (solid cylinder) of mass $$M$$ and radius $$R is $$spun up from rest to angular speed $$\omega by a $$constant torque $$\tau. $$How much time $$t$$ does it take to reach this speed?

$$t = \frac{M R^2$ \omega}{2 \tau}$$

Question 1

A wind turbine blade rotates about its central axis. If the tip of the blade is twice as far from the axis as a point halfway along the blade, how does the linear speed at the tip compare to the linear speed halfway along the blade, assuming both points have the same angular velocity $$\omega$$?

Accepted Answer

The tip moves at twice the linear speed of the halfway point.

Question 2

A particle moves along a circular path of radius $$r. If $$the particle travels an arc length $$s$$, what is the angular displacement $$	heta in $$radians?

Accepted Answer

$$	heta = s/r$$

Question 3

A wheel rotates with a constant angular acceleration $$\alpha. If $$its initial angular velocity is $$\$$omega_0$$ and it rotates through an angular displacement $$\Delta 	heta$$ in time t$, which equation correctly relates these quantities?

Accepted Answer

$$\Delta 	heta = \$$omega_0$$ t + \frac{1}{2} \alpha t^2$

Question 4

A door is pushed with a force $$F at a $$distance $$r$$ from the hinge, at an angle $$\phi to $$the radial line. What is the torque $$	au$$ produced by this force?

Accepted Answer

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

Question 5

A uniform rod of length $$L$$ and mass $$M$$ rotates about one end. What is its moment of inertia $$I$$ about that end?

Accepted Answer

$$I = \frac{1}{3} M L^2$

Question 6

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 where the pole is attached. What is the magnitude of the gravitational torque about the point of attachment? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$	au = (3.2)(9.8)(1.6) \sin 25^\circ$$

Question 7

A seesaw is balanced with a 22 kg child sitting 1.6 m from the pivot on one side. Where should a 25 kg child sit on the other side to balance the seesaw, assuming the seesaw's mass is negligible?

Accepted Answer

At $$x = \frac{22}{25} 	imes 1.6\ \mathrm{m}$$ from the pivot

Question 8

A solid cylinder (mass $$M$$, radius $$R) is $$spun up from rest by a constant torque $$	au. $$What is the angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \frac{2	au}{M R^2$}$$

Question 9

A bucket of mass $$m is $$attached to a rope wound around a cylinder of mass $$M$$ and radius $$R. $$When the bucket is released, what is the acceleration $$a of $$the bucket as it falls, assuming the rope does not slip?

Accepted Answer

$$a = \frac{m}{m + \frac{1}{2} M} g$$

Question 10

A wheel of radius $$R$$ rolls without slipping at a speed $$v. $$What is the angular velocity $$\omega of $$the wheel?

Accepted Answer

$$\omega = \frac{v}{R}$$

Question 11

A force $$F is $$applied perpendicular to a wrench at a distance $$r$$ from the pivot. If the force is doubled and the distance is halved, what happens to the torque?

Accepted Answer

The torque remains the same.

Question 12

Which of the following statements about the moment of inertia is correct?

Accepted Answer

It depends on both the mass and how the mass is distributed relative to the axis of rotation.

Question 13

A gymnast rotates about a bar. The gravitational torque on her body can be calculated by assuming her weight acts at which point?

Accepted Answer

At her center of gravity

Question 14

A rolling wheel moves forward one circumference in one revolution. If the radius of the wheel is $$R$$ and the angular velocity is $$\omega$$, what is the velocity of the center of mass?

Accepted Answer

$$v = \omega R$$

Question 15

A force is applied at an angle to a wrench. Which component of the force is responsible for producing torque?

Accepted Answer

The component perpendicular to the wrench

Question 16

A uniform disk and a uniform hoop, both with the same mass and radius, are spun about their central axes. Which has the greater moment of inertia?

Accepted Answer

The hoop

Question 17

A flywheel (solid cylinder) of mass $$M$$ and radius $$R is $$spun up from rest to angular speed $$\omega by a $$constant torque $$	au. $$How much time $$t$$ does it take to reach this speed?

Accepted Answer

$$t = \frac{M R^2$ \omega}{2 	au}$$

Question 18

A rod of length $$L$$ and mass $$M is $$pivoted at one end and held horizontally. What is the torque due to gravity about the pivot?

Accepted Answer

$$	au = \frac{1}{2} M g L$$

Rotational Motion and Dynamics: Physics with Calculus Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards