Q: If the line of action of a force passes through the axis of rotation, what is the torque produced by this force?

Zero, because $$\sin \theta = 0$$ when $$\theta = 0$$

Question 1

Which of the following best describes the physical meaning of the moment of inertia $$I$$ for a rigid body rotating about a fixed axis?

Accepted Answer

It is a measure of the resistance of a body to changes in its rotational motion, given by $$I = \int r^2$ dm.$$

Question 2

A thin uniform rod of length $$L$$ and mass $$M$$ rotates about an axis perpendicular to the rod and passing through one end. What is its moment of inertia?

Accepted Answer

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

Question 3

The parallel axis theorem relates the moment of inertia $$I_p$$ about any axis to the moment of inertia $$I_{cm}$$ about a parallel axis through the center of mass. Which equation correctly expresses this theorem?

Accepted Answer

$$I_p = I_{cm} + Md^2$

Question 4

A flywheel is used to store energy in a solar power plant. If the flywheel has a moment of inertia $$I$$ and rotates with angular velocity $$\omega$$, what is the rotational kinetic energy stored?

Accepted Answer

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

Question 5

A force $$F is $$applied tangentially at a distance $$r$$ from the axis of rotation of a wheel. What is the torque $$	au$$ produced by this force?

Accepted Answer

$$	au = rF \sin 	heta$$

Question 6

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

Accepted Answer

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

Question 7

If a rigid body is rotating with angular acceleration $$\alpha$$ and has a moment of inertia $$I$$, what is the net torque $$	au$$ acting on it?

Accepted Answer

$$	au = I\alpha$$

Question 8

A solar power plant uses a flywheel to regulate power output. If the flywheel stores $$100$$ kWh of energy and operates at an angular velocity $$\omega$$, what happens to the stored energy if $$\omega is $$doubled?

Accepted Answer

The stored energy increases by a factor of 4.

Question 9

Which of the following statements about rotational kinetic energy is correct?

Accepted Answer

It depends on both the moment of inertia and the square of the angular velocity.

Question 10

A wheel is subjected to a net torque of $$120 N$$·m. If its moment of inertia is $$40 kg$$·m$$^2$$, what is its angular acceleration?

Accepted Answer

$$\alpha = 3$$ rad/s$$^2$$

Question 11

A uniform disk and a uniform sphere have the same mass and radius. Which one has the greater moment of inertia about its central axis?

Accepted Answer

The disk, because $$I_{disk} = \frac{1}{2}MR^2$ and I$$_{sphere} = \frac{2}{5}$$MR^2.$$

Question 12

A solar power plant experiences fluctuations in sunlight. Which physical principle allows a flywheel to help regulate the power output?

Accepted Answer

Conservation of angular momentum and energy storage in rotational motion.

Question 13

A force of $$800 N is $$applied perpendicular to a lever arm of length $$2.00 m. $$What is the resulting torque?

Accepted Answer

$$	au = 1600 N$$·m

Question 14

A cylindrical shell of radius $$r$$ and thickness $$dr$$ has mass $$dm. $$What is the contribution to the moment of inertia from this shell?

Accepted Answer

$$dI = r^2$ dm$$

Question 15

If the line of action of a force passes through the axis of rotation, what is the torque produced by this force?

Accepted Answer

Zero, because $$\sin 	heta = 0$$ when $$	heta = 0$$

Question 16

A rigid body rotates with constant angular velocity $$\omega. $$What is its angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = 0$$

Question 17

Which of the following is the correct expression for the angular velocity $$\omega in $$terms of the angle $$	heta$$ and time $$t$$ for constant angular acceleration $$\alpha$$?

Accepted Answer

$$\omega = \$$omega_0$$ + \alpha t$$

Question 18

A solar power plant generates $$10.0 MW of $$power. If the energy produced in a year is $$E_{2012} = 14400$$ MWh, what is the average number of hours per year the plant operates at full power?

Accepted Answer

1440 hours

Question 19

A flywheel in a solar power plant has a storage capacity of $$100$$ kWh and an output of $$300 kW. $$For how many hours can it supply power at full output before being depleted?

Accepted Answer

0.33 hours

Rotational Motion and Dynamics of Rigid Bodies

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