Q: A seesaw is $$3.0\ \mathrm{m}$$ long. You have a mass of $$90\ \mathrm{kg}$$ and your friend has a mass of $$60\ \mathrm{kg}. $$Where should the pivot be placed so the seesaw balances?

$$x = 1.2\ \mathrm{m}$$\ \text{from your side}$$

Q: A mobile sculpture consists of two $$2.0\ \mathrm{kg}$$ spheres and a $$3.0\ \mathrm{kg}$$ rod of length $$4.0\ \mathrm{m}$$, rotating at $$3$$ revolutions per minute. What is the angular velocity in $$\mathrm{rad/s}$$?

$$\omega = \dfrac{2\pi \times 3}{60} = 0.314\ \mathrm{rad/s}$$

Q: A $$300\ \mathrm{kg}$$ flywheel with $$I = 580\ \mathrm{kg\cdot m^2$}$$ starts from rest. After $$4.00$$ revolutions under a constant torque of $$2000\ \mathrm{N\cdot m}$$, what is its angular velocity?

$$\omega = \sqrt{2\alpha \Delta \theta}$$, where $$\alpha = \dfrac{2000}{580}$$ and $$\Delta \theta = 4 \times 2\pi$$

Q: A $$2.0\ \mathrm{kg}$$ sphere is attached to a $$3.0\ \mathrm{kg}$$ rod of length $$4.0\ \mathrm{m}$$, rotating about its midpoint. What is the moment of inertia of the system?

$$I = 2 \times 2.0 \times (2.0)^2$ + \dfrac{1}{12} \times 3.0 \times (4.0)^2$

Q: Which condition must be satisfied for a rigid body to be in complete equilibrium?

$$\sum F_x = 0$$, $$\sum F_y = 0$$, and $$\sum \tau = 0$$

Question 1

A flywheel of a motor has a moment of inertia of $$580\ \mathrm{kg\cdot m^2$}$$ and a constant torque of $$2000\ \mathrm{N\cdot m} is $$applied. What is the angular acceleration of the flywheel?

Accepted Answer

$$\alpha = \dfrac{2000}{580}\ \mathrm{$$rad/s^2$$}$$

Question 2

Which equation correctly relates torque ($$	au$$), moment of inertia ($$I$$), and angular acceleration ($$\alpha$$)?

Accepted Answer

$$	au = I\alpha$$

Question 3

A rigid body rotates with angular velocity $$\omega$$ and has moment of inertia $$I. $$What is its angular momentum?

Accepted Answer

$$L = I\omega$$

Question 4

If a torque of $$50\ \mathrm{N\cdot m} is $$applied for $$10\ \mathrm{s}$$, what is the change in angular momentum of the system?

Accepted Answer

$$\Delta L = 500\ \mathrm{N\cdot m\cdot s}$$

Question 5

A seesaw is $$3.0\ \mathrm{m}$$ long. You have a mass of $$90\ \mathrm{kg}$$ and your friend has a mass of $$60\ \mathrm{kg}. $$Where should the pivot be placed so the seesaw balances?

Accepted Answer

$$x = 1.2\ \mathrm{m}$$\ 	ext{from your side}$$

Question 6

A mobile sculpture consists of two $$2.0\ \mathrm{kg}$$ spheres and a $$3.0\ \mathrm{kg}$$ rod of length $$4.0\ \mathrm{m}$$, rotating at $$3$$ revolutions per minute. What is the angular velocity in $$\mathrm{rad/s}$$?

Accepted Answer

$$\omega = \dfrac{2\pi 	imes 3}{60} = 0.314\ \mathrm{rad/s}$$

Question 7

If the sum of all external torques on a system is zero, what happens to the system's angular momentum?

Accepted Answer

It is conserved.

Question 8

A professor spins on a turntable with arms outstretched, then pulls the dumbbells close to their chest. What happens to their angular velocity?

Accepted Answer

It increases.

Question 9

Which of the following is the correct expression for rotational work done by a constant torque $$	au$$ over an angle $$\Delta 	heta$$?

Accepted Answer

$$W = 	au \Delta 	heta$$

Question 10

A $$300\ \mathrm{kg}$$ flywheel with $$I = 580\ \mathrm{kg\cdot m^2$}$$ starts from rest. After $$4.00$$ revolutions under a constant torque of $$2000\ \mathrm{N\cdot m}$$, what is its angular velocity?

Accepted Answer

$$\omega = \sqrt{2\alpha \Delta 	heta}$$, where $$\alpha = \dfrac{2000}{580}$$ and $$\Delta 	heta = 4 	imes 2\pi$$

Question 11

Which of the following is NOT a correct way to calculate torque?

Accepted Answer

$$	au = F \cos \phi$$

Question 12

A child pushes a merry-go-round with a constant tangential force, causing it to rotate. Which formula gives the power delivered to the system?

Accepted Answer

$$P = 	au \omega$$

Question 13

A $$2.0\ \mathrm{kg}$$ sphere is attached to a $$3.0\ \mathrm{kg}$$ rod of length $$4.0\ \mathrm{m}$$, rotating about its midpoint. What is the moment of inertia of the system?

Accepted Answer

$$I = 2 	imes 2.0 	imes (2.0)^2$ + \dfrac{1}{12} 	imes 3.0 	imes (4.0)^2$

Question 14

Which statement about the right-hand rule for angular vectors is correct?

Accepted Answer

Curl the fingers of your right hand in the direction of rotation; your thumb points in the direction of the angular vector.

Question 15

A board of length $$2.00\ \mathrm{m} is $$lifted at one end with $$400\ \mathrm{N}$$ and at the other with $$600\ \mathrm{N}. $$What is the weight of the motor placed on the board?

Accepted Answer

$$W = 400 + 600 = 1000\ \mathrm{N}$$

Question 16

Which condition must be satisfied for a rigid body to be in complete equilibrium?

Accepted Answer

$$\sum F_x = 0$$, $$\sum F_y = 0$$, and $$\sum 	au = 0$$

Question 17

A $$5.0\ \mathrm{kg}$$ dumbbell is held $$1.0\ \mathrm{m}$$ from the axis and then moved to $$0.20\ \mathrm{m}. If $$the moment of inertia drops from $$3.0\ \mathrm{kg\cdot m^2$} to$$ $$2.2\ \mathrm{kg\cdot m^2$}$$, what happens to the kinetic energy if angular momentum is conserved?

Accepted Answer

Kinetic energy increases.

Question 18

Which of the following best describes the vector nature of torque?

Accepted Answer

Torque has both magnitude and direction, and follows the right-hand rule.

Dynamics of Rotational Motion: Torque, Angular Momentum, and Equilibrium

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