Q: If a net torque $$\sum \tau_z is $$applied to a rigid body with moment of inertia $$I$$, what is the resulting angular acceleration $$\alpha_z$$?

$$\alpha_z = \frac{\sum \tau_z}{I}$$

Q: A force of $$F_1 = 8.00$$\ \mathrm{N}$$ is applied downward at the end of a 3.00$$\ \mathrm{m}$$ rod, and F_2$ = 12.0\ \mathrm{N} is $$applied at $$2.00\ \mathrm{m}$$ from the pivot at a $$30.0^\circ$$ angle. What is the net torque about the pivot $$O$$?

$$\tau_{net} = 12.0 \times 2.00 \times \sin 30.0^\circ - 8.00 \times 3.00$$

Question 1

Which of the following best describes the moment of inertia ($$I) $$for a rigid body?

Accepted Answer

$$I is $$the sum of each mass element times the square of its distance from the axis: $$I = \sum_i m_i r_i^2$ = \int r^2$ dm$$

Question 2

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

Accepted Answer

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

Question 3

The parallel axis theorem relates the moment of inertia about any axis to that about a parallel axis through the center of mass. Which formula expresses this theorem?

Accepted Answer

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

Question 4

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 5

A force $$\vec{F} is $$applied at a distance $$r$$ from a pivot point, making an angle $$\phi$$ with the lever arm. What is the torque $$	au$$ about the pivot?

Accepted Answer

$$	au = rF\sin\phi$$

Question 6

The rotational kinetic energy of a rigid body is given by which formula?

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

If a net torque $$\sum 	au_z is $$applied to a rigid body with moment of inertia $$I$$, what is the resulting angular acceleration $$\alpha_z$$?

Accepted Answer

$$\alpha_z = \frac{\sum 	au_z}{I}$$

Question 10

A force of $$F_1 = 8.00$$\ \mathrm{N}$$ is applied downward at the end of a 3.00$$\ \mathrm{m}$$ rod, and F_2$ = 12.0\ \mathrm{N} is $$applied at $$2.00\ \mathrm{m}$$ from the pivot at a $$30.0^\circ$$ angle. What is the net torque about the pivot $$O$$?

Accepted Answer

$$	au_{net} = 12.0 	imes 2.00 	imes \sin 30.0^\circ - 8.00 	imes 3.00$$

Question 11

Which of the following statements about the flywheel energy storage system is correct?

Accepted Answer

The flywheel stores energy as rotational kinetic energy.

Question 12

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

Accepted Answer

$$I = MR^2$

Question 13

If a rigid body rotates with angular velocity $$\omega$$ and angular acceleration $$\alpha$$, what is the linear acceleration $$a of a $$point at distance $$r$$ from the axis?

Accepted Answer

$$a = r\alpha$$

Question 14

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

Accepted Answer

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

Question 15

Which of the following best describes the relationship between torque and angular acceleration for a rigid body?

Accepted Answer

$$\sum 	au = I\alpha$$

Question 16

A solar power plant uses a flywheel to store excess energy during the day and release it at night. If the flywheel's angular velocity doubles, by what factor does its stored energy increase?

Accepted Answer

The stored energy increases by a factor of 4.

Rotatie van Starre Lichamen & Dynamica van de Rotatiebeweging

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