Question 1

A uniform rod of length $$3\ \mathrm{m} is $$acted upon by four forces: $$F_1 = 2$$\ \mathrm{N}$$ at 0$$\ \mathrm{m}$$, F_2$ = 4\ \mathrm{N} at$$ $$1\ \mathrm{m} ($$perpendicular), $$F_3 = 4$$\ \mathrm{N}$$ at 2$$\ \mathrm{m}$$ (at 30$$^\circ$$ below the rod), and F_4$ = 2\ \mathrm{N} at$$ $$3\ \mathrm{m} ($$parallel to the rod). What is the net torque about the left end of the rod?

Accepted Answer

$$0\ \mathrm{N\cdot m}$$

Question 2

A person holds a $$5\ \mathrm{kg}$$ weight in their hand with their forearm horizontal. The biceps attaches $$4\ \mathrm{cm}$$ from the elbow at an angle of $$105^\circ to $$the forearm. The forearm and hand together have a mass of $$1.5\ \mathrm{kg}$$, with their center of gravity $$12\ \mathrm{cm}$$ from the elbow. What is the force exerted by the biceps muscle?

Accepted Answer

$$433\ \mathrm{N}$$

Question 3

A leg in a cast (mass $$15.0\ \mathrm{kg}$$, center of gravity $$35.0\ \mathrm{cm}$$ from the hip) is suspended by a sling $$78.0\ \mathrm{cm}$$ from the hip. What mass $$m$$ should be hung from the sling to balance the leg?

Accepted Answer

$$6.73\ \mathrm{kg}$$

Question 4

Which of the following best describes the moment of inertia for a system of particles?

Accepted Answer

$$I = \sum_i m_i r_i^2$

Question 5

A dumbbell consists of two masses $$m$$ connected by a massless rod of length $$R. $$What is the moment of inertia about an axis through the center of the rod and perpendicular to it?

Accepted Answer

$$I = mR^2$

Question 6

Which of the following objects is hardest to rotate about its center: a solid sphere, a solid cylinder, or a thin hoop, all with the same mass and radius?

Accepted Answer

The thin hoop

Question 7

A force $$F is $$applied at a distance $$r$$ from the axis of rotation, making an angle $$	heta$$ with the lever arm. What is the torque produced?

Accepted Answer

$$	au = rF\sin	heta$$

Question 8

A uniform 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$

Question 9

A solid disk and a thin hoop, both with mass $$M$$ and radius $$R$$, roll down an incline. Which reaches the bottom first and why?

Accepted Answer

The solid disk, because it has a smaller moment of inertia

Question 10

Which of the following statements about torque is correct?

Accepted Answer

Torque is positive if it causes counterclockwise rotation

Question 11

A force of $$20\ \mathrm{N} is $$applied at $$2\ \mathrm{m}$$ from the axis of rotation at an angle of $$60^\circ to $$the lever arm. What is the magnitude of the torque?

Accepted Answer

$$34.6\ \mathrm{N\cdot m}$$

Question 12

Which dumbbell has the larger moment of inertia about the midpoint of the rod? (A: two masses $$m at $$distance $$R$$; B: two masses $$m/2 at $$distance $$2R)$$

Accepted Answer

Dumbbell B

Question 13

A dumbbell-shaped object is composed of two equal masses $$m$$ connected by a rod of negligible mass and length $$R. If$$ $$I_1 is $$the moment of inertia about the center and $$I_2$$ about one mass, which is true?

Accepted Answer

$$I_2$$ \u003e $$I_1$$

Question 14

The moment of inertia of a solid body depends on which of the following?

Accepted Answer

Both the mass and its distribution relative to the axis

Question 15

Which equation correctly relates torque, moment of inertia, and angular acceleration?

Accepted Answer

$$	au = I\alpha$$

Question 16

A force is applied to a door at a distance $$r$$ from the hinge. To maximize the torque, at what angle should the force be applied?

Accepted Answer

$$90^\circ to $$the door (perpendicular)

Question 17

A uniform rod of length $$L$$ and mass $$M$$ rotates about its center. What is its moment of inertia?

Accepted Answer

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

Question 18

Which of the following is the correct SI unit for moment of inertia?

Accepted Answer

$$\mathrm{kg\cdot m^2$}$$

Question 19

A force of $$10\ \mathrm{N} is $$applied tangentially to a wheel of radius $$0.5\ \mathrm{m}. $$What is the resulting torque?

Accepted Answer

$$5\ \mathrm{N\cdot m}$$

Torque and Moment of Inertia: Rotational Dynamics Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards