Q: Which of the following best describes the relationship between linear displacement $$\Delta x$$ and angular displacement $$\Delta \theta$$ for an object moving along a circular path of radius $$r$$?

$$\Delta x = r \cdot \Delta \theta$$

Q: A wheel of radius $$5 m $$accelerates from $$60$$ RPM to $$180$$ RPM in $$2 s. $$What is its angular acceleration in $$\text{rad}/\text{s}^2$$?

$$6.28\ \text{rad}/\text{s}^2$$

Q: A clock's minute hand completes one revolution every hour. What is its rotational velocity in rad/s?

$$0.00175\ \text{rad}/\text{s}$$

Question 1

Which of the following best describes the relationship between linear displacement $$\Delta x$$ and angular displacement $$\Delta 	heta$$ for an object moving along a circular path of radius $$r$$?

Accepted Answer

$$\Delta x = r \cdot \Delta 	heta$$

Question 2

A car tire of radius $$0.40 m $$rotates $$10,000$$ times as you drive. How far did you drive, in meters?

Accepted Answer

$$25,120 m$$

Question 3

An object moves a total distance of $$1,000 m $$around a circle of radius $$30 m. $$How many degrees does the object go through?

Accepted Answer

$$1,910^\circ$$

Question 4

Which equation correctly links linear velocity $$v$$ and angular velocity $$\omega$$ for a point at a distance $$r$$ from the axis of rotation?

Accepted Answer

$$v = r \cdot \omega$$

Question 5

A wheel of radius $$5 m $$accelerates from $$60$$ RPM to $$180$$ RPM in $$2 s. $$What is its angular acceleration in $$	ext{rad}/	ext{s}^2$$?

Accepted Answer

$$6.28\ 	ext{rad}/	ext{s}^2$$

Question 6

A disc of radius $$10 m $$rotates at $$180$$ RPM. What is the linear speed at a point $$7 m $$from the center?

Accepted Answer

$$131.9\ 	ext{m/s}$$

Question 7

A rock rotates around a light, $$4-m $$long string. The rock is initially at rest, but reaches $$150$$ RPM in $$3 s. $$What is its tangential acceleration after $$3 s$$?

Accepted Answer

$$20.94\ 	ext{m/s}^2$$

Question 8

Which of the following is the correct formula for torque $$	au$$ produced by a force $$F$$ applied at a distance $$r$$ from the axis, at an angle $$	heta$$?

Accepted Answer

$$	au = r F \sin 	heta$$

Question 9

You pull with $$100 N at $$the edge of a $$25 cm $$long wrench, at an angle of $$53^\circ. $$What torque do you produce about the axis perpendicular to the wrench and through the bolt?

Accepted Answer

$$20.0\ 	ext{Nm}$$

Question 10

A $$3-m $$wide door is pushed with $$10 N at $$the edge, perpendicular to the door. What is the torque produced?

Accepted Answer

$$30\ 	ext{Nm}$$

Question 11

An object of negligible size moves in a circular path of radius $$20 m $$with $$90$$ RPM. What is its radial acceleration?

Accepted Answer

$$177.8\ 	ext{m/s}^2$$

Question 12

A $$30-kg $$disc of radius $$2 m $$rotates at a constant $$120$$ RPM. What is its period?

Accepted Answer

$$0.5\ 	ext{s}$$

Question 13

A $$4-m $$long blade initially at rest begins to spin with $$3\ 	ext{rad}/	ext{s}^2$$ around its axis, located at the middle of the blade. It accelerates for $$10 s. $$What is the tangential speed at the tip of the blade after $$10 s$$?

Accepted Answer

$$60\ 	ext{m/s}$$

Question 14

A carousel $$10 m in $$radius completes one cycle every $$45 s. $$What is the angular velocity?

Accepted Answer

$$0.140\ 	ext{rad}/	ext{s}$$

Question 15

A $$2-m $$long bar is free to rotate about an axis located $$0.7 m $$from one end. Two forces act on the bar, $$F_1 = 100$ N and F_2$ = 200 N$$, both at $$30^\circ$$ with the bar. What is the net torque on the bar?

Accepted Answer

$$181.3\ 	ext{Nm}$$

Question 16

A wheel of radius $$8 m $$spins around its central axis at $$10$$ rad/s. What is the linear speed at the edge of the wheel?

Accepted Answer

$$80\ 	ext{m/s}$$

Question 17

A clock's minute hand completes one revolution every hour. What is its rotational velocity in rad/s?

Accepted Answer

$$0.00175\ 	ext{rad}/	ext{s}$$

Question 18

A force of $$40 N is $$applied at the end of a $$3 m $$long fishing pole, at $$20^\circ$$ below the $$+x$$ axis. What is the torque produced about the axis of rotation?

Accepted Answer

$$40.98\ 	ext{Nm}$$

Rotational Motion and Torque: Study Guide for College Physics

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