Q: A Blu-ray disc slows down from an initial angular velocity of $$\$$omega_0$$ = 27.5\ \text{rad/s}$$ with a constant angular acceleration $$\alpha = -10\ \text{rad/s}^2. $$What is its angular velocity after $$t = 0.3\ \text{s}$$?

$$\omega = 26.9\ \text{rad/s}$$

Q: A point on a centrifuge is $$r = 0.10\ \text{m}$$ from the axis and moves at $$v = 150\ \text{m/s}. $$What is the angular velocity $$\omega of $$the centrifuge?

$$\omega = 1500\ \text{rad/s}$$

Q: A wrench is $$0.15\ \text{m}$$ long. A force of $$150\ \text{N} is $$applied at $$60^\circ$$ above the horizontal. What is the magnitude of the torque?

$$\tau = 11.3\ \text{N} \cdot \text{m}$$

Q: A cable drum (solid cylinder) of mass $$M = 50\ \text{kg}$$ and radius $$R = 0.12\ \text{m} is $$acted on by a force $$F = 9.0\ \text{N} at $$its rim. What is the torque?

$$\tau = 1.08\ \text{N} \cdot \text{m}$$

Q: A point $$P on a $$rotating disc is $$r$$ meters from the axis. If the disc rotates at angular speed $$\omega$$, what is the centripetal acceleration of $$P$$?

$$a_{\text{rad}} = \$$omega^2$$ r$$

Question 1

A Blu-ray disc slows down from an initial angular velocity of $$\$$omega_0$$ = 27.5\ 	ext{rad/s}$$ with a constant angular acceleration $$\alpha = -10\ 	ext{rad/s}^2. $$What is its angular velocity after $$t = 0.3\ 	ext{s}$$?

Accepted Answer

$$\omega = 26.9\ 	ext{rad/s}$$

Question 2

A point on a centrifuge is $$r = 0.10\ 	ext{m}$$ from the axis and moves at $$v = 150\ 	ext{m/s}. $$What is the angular velocity $$\omega of $$the centrifuge?

Accepted Answer

$$\omega = 1500\ 	ext{rad/s}$$

Question 3

Which equation correctly relates the linear speed $$v of a $$point on a rotating rigid body to its angular speed $$\omega$$ and distance $$r$$ from the axis?

Accepted Answer

$$v = r \omega$$

Question 4

A solid sphere and a hollow sphere have the same mass $$M$$ and radius $$R. $$Which has the greater moment of inertia?

Accepted Answer

The hollow sphere

Question 5

What is the moment of inertia $$I of a $$slender rod of mass $$M$$ and length $$L$$ about its center?

Accepted Answer

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

Question 6

A wrench is $$0.15\ 	ext{m}$$ long. A force of $$150\ 	ext{N} is $$applied at $$60^\circ$$ above the horizontal. What is the magnitude of the torque?

Accepted Answer

$$	au = 11.3\ 	ext{N} \cdot 	ext{m}$$

Question 7

Which force produces the greatest magnitude of torque about point $$O in $$the diagram where all forces have equal magnitude?

Accepted Answer

$$F_4$$

Question 8

What is the rotational kinetic energy $$K of a $$rigid body with moment of inertia $$I$$ rotating at angular speed $$\omega$$?

Accepted Answer

$$K = \frac{1}{2} I \$$omega^2$$

Question 9

A solid cylinder of mass $$M$$ and radius $$R$$ rotates about its axis. What is its moment of inertia?

Accepted Answer

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

Question 10

If a net torque $$	au$$ acts on a disc with moment of inertia $$I$$, what is its angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = 	au / I$$

Question 11

A cable drum (solid cylinder) of mass $$M = 50\ 	ext{kg}$$ and radius $$R = 0.12\ 	ext{m} is $$acted on by a force $$F = 9.0\ 	ext{N} at $$its rim. What is the torque?

Accepted Answer

$$	au = 1.08\ 	ext{N} \cdot 	ext{m}$$

Question 12

Which statement about moment of inertia is correct?

Accepted Answer

It depends on both mass and how far the mass is from the axis.

Question 13

A thin-walled hollow cylinder of mass $$M$$ and radius $$R$$ rotates about its axis. What is its moment of inertia?

Accepted Answer

$$I = MR^2$

Question 14

If a force is applied perpendicular to a wrench at a distance $$r$$ from the axis, what is the torque produced?

Accepted Answer

$$	au = F r \sin 	heta$$

Question 15

A solid sphere of mass $$M$$ and radius $$R$$ rolls without slipping. What is its moment of inertia?

Accepted Answer

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

Question 16

Which of the following best describes the effect of mass distribution on rotational motion?

Accepted Answer

Mass farther from the axis increases moment of inertia.

Question 17

Under the influence of a constant net torque about a stationary axis, an object will move with:

Accepted Answer

Constant angular acceleration

Question 18

A point $$P on a $$rotating disc is $$r$$ meters from the axis. If the disc rotates at angular speed $$\omega$$, what is the centripetal acceleration of $$P$$?

Accepted Answer

$$a_{	ext{rad}} = \$$omega^2$$ r$$

Question 19

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

Accepted Answer

$$I = \frac{1}{3}ML^2$

Rotation of Rigid Bodies and Torque – Study Notes

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