Q: A door is 0.8 m wide. You push with a force of 100 N perpendicular to the door at its edge. What is the torque $$\tau$$ you apply?

$$\tau = 80\ \mathrm{N\cdot m}$$

Q: A gymnast hangs from a bar, and her center of gravity is 1.2 m from the axis of rotation. If her mass is 50 kg, what is the magnitude of the gravitational torque about the axis?

$$\tau = 588\ \mathrm{N\cdot m}$$

Q: A force of 4200 N is applied to the top of a 17 m tall statue at an angle of $$65^\circ to $$the horizontal. What is the torque about the base?

$$4200 \times 17 \times \sin 65^\circ\ \mathrm{N\cdot m}$$

Question 1

A cyclist is racing on a velodrome track. If the radius of the track is 25 m and the cyclist completes one lap in 20 seconds, what is the angular velocity $$\omega of $$the cyclist?

Accepted Answer

$$\omega = 0.314\ \mathrm{rad/s}$$

Question 2

A wind turbine blade is 50 m long and rotates at 10 rpm. What is the speed $$v of $$the tip of the blade?

Accepted Answer

$$v = 52\ \mathrm{m/s}$$

Question 3

A particle moves along a circular path of radius $$r$$ and subtends an angle $$	heta at $$the center. What is the arc length $$s$$ traveled by the particle?

Accepted Answer

$$s = r	heta$$

Question 4

A door is 0.8 m wide. You push with a force of 100 N perpendicular to the door at its edge. What is the torque $$	au$$ you apply?

Accepted Answer

$$	au = 80\ \mathrm{N\cdot m}$$

Question 5

A gymnast hangs from a bar, and her center of gravity is 1.2 m from the axis of rotation. If her mass is 50 kg, what is the magnitude of the gravitational torque about the axis?

Accepted Answer

$$	au = 588\ \mathrm{N\cdot m}$$

Question 6

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

Accepted Answer

$$I = \frac{1}{12}ML^2$

Question 7

A solid sphere of mass $$M$$ and radius $$R$$ rotates about its diameter. What is its moment of inertia $$I$$?

Accepted Answer

$$I = \frac{2}{5}MR^2$

Question 8

A merry-go-round spins at a constant angular velocity. If a child moves from the center to the edge, what happens to the child’s speed?

Accepted Answer

It doubles.

Question 9

A wheel starts from rest and accelerates at a constant angular acceleration $$\alpha. $$After time $$t$$, its angular velocity is $$\omega. $$What is its angular velocity after time $$2t$$?

Accepted Answer

$$2\omega$$

Question 10

A 3.2 kg flagpole is attached to a wall at an angle of $$25^\circ$$ above the horizontal. Its center of gravity is 1.6 m from the wall. What is the moment arm for the gravitational force?

Accepted Answer

$$1.45\ \mathrm{m}$$

Question 11

A wrench of length $$r is $$used to loosen a bolt. If you apply a force $$F at an $$angle $$\phi to $$the wrench, what is the torque $$	au$$?

Accepted Answer

$$	au = rF\sin\phi$$

Question 12

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

Accepted Answer

$$\omega = v/R$$

Question 13

A seesaw is balanced with a 22 kg child sitting 1.6 m from the pivot. Where should a 25 kg child sit to balance the seesaw?

Accepted Answer

1.4 m from the pivot on the opposite side

Question 14

A fan blade is slowing down. If $$\omega is $$positive, what is the sign of the angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha is $$negative

Question 15

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.

Question 16

A force of 4200 N is applied to the top of a 17 m tall statue at an angle of $$65^\circ to $$the horizontal. What is the torque about the base?

Accepted Answer

$$4200 	imes 17 	imes \sin 65^\circ\ \mathrm{N\cdot m}$$

Question 17

A uniform disk of mass $$M$$ and radius $$R$$ rotates about its center. What is its moment of inertia $$I$$?

Accepted Answer

$$I = \frac{1}{2}MR^2$

Question 18

A car tire has a radius of 0.3 m and the car moves at 29 m/s. What is the angular speed $$\omega of $$the tire?

Accepted Answer

$$\omega = 97\ \mathrm{rad/s}$$

Chapter 7: Rotational Motion – Physics with Algebra Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards