Question 1

A weight is tied to a rope wrapped around a pulley that is initially rotating counterclockwise and pulling the weight up. The tension in the rope creates a constant torque that opposes the rotation. Which of the following best describes the angular acceleration $$\alpha of $$the pulley during the motion until the weight returns to its original height?

Accepted Answer

$$\alpha is $$constant and negative.

Question 2

Given an angular velocity versus time graph that is a straight line with a negative slope, what does the corresponding angular acceleration versus time graph look like?

Accepted Answer

A horizontal line below the time axis.

Question 3

Six small spheres (three brass, three aluminum) are connected by three mutually perpendicular rods to form a jack. All spheres are the same distance from the origin, and the rods are massless. Which arrangement will have the greatest moment of inertia about the x-axis?

Accepted Answer

The arrangement with all four brass spheres not on the x-axis.

Question 4

Three flat objects—a circular ring, a circular disc, and a square loop—each have mass $$M$$ and outer dimension $$2R. $$The axis of rotation passes through the center and is perpendicular to the plane. Rank their moments of inertia from greatest to least.

Accepted Answer

Square loop $$\u003e$$ Circular ring $$\u003e$$ Circular disc

Question 5

A wheel is made of two pulleys of different radii, $$a$$ and $$b$$ ($$b \u003e a$$), attached together. Each has a string with a weight hanging from it. When released, the wheel accelerates counterclockwise. What can you conclude about the torques produced by the two weights?

Accepted Answer

The torque from the weight on the smaller pulley is greater.

Question 6

Several hollow spheres of equal mass but different radii roll without slipping at different linear speeds $$v$$ and angular speeds $$\omega. $$Which formula correctly relates the radius $$R to$$ $$v$$ and $$\omega$$ for each sphere?

Accepted Answer

$$R = \dfrac{v}{\omega}$$

Question 7

Three equal forces are applied to a 3-m by 2-m rectangle at different points and angles. Which statement is true about the net torque about point B?

Accepted Answer

The net torque is zero.

Question 8

A hollow sphere and a solid sphere of equal mass and diameter are released from rest at the top of a ramp. Which will reach the bottom first, and why?

Accepted Answer

The solid sphere, because it has a smaller moment of inertia.

Question 9

A fishing rod is balanced on a finger at a point closer to the handle than the tip. If the rod is cut at the balance point, how do the weights of the two pieces compare?

Accepted Answer

The piece with the handle is heavier.

Question 10

Four signs of different masses are suspended from rods of equal length at various angles from a building. Which factor most directly determines the torque each sign exerts about the attachment point?

Accepted Answer

The product of the sign's weight and the perpendicular distance from the attachment point.

Question 11

Four forces act on a hexagonal plywood sheet, each at a different location. Which force produces the greatest torque about the center?

Accepted Answer

The force with the largest perpendicular distance from the center.

Question 12

A balance beam has two keys 6 cm from the pivot on the left and three keys 5 cm from the pivot on the right. What happens when the beam is released?

Accepted Answer

It rotates clockwise.

Question 13

A rod is made of three segments of equal length with masses $$m$$, $$2m$$, and $$3m$$ from left to right. About which end is the moment of inertia greater?

Accepted Answer

About the left end.

Question 14

A massless rod is supported by a fulcrum and a 200-kg mass is suspended from the left end. The rod is held at rest by a downward force $$F on $$the right end. If the rod is shortened but the positions of the mass and force remain proportional, what happens to the required force $$F$$?

Accepted Answer

It remains the same.

Question 15

A 2-m long massless rod supports a 12-N weight. The left end is pinned, and a vertical force $$F$$ holds the rod at rest. If the weight is twice as far from the pivot as the applied force, what is the magnitude of $$F$$?

Accepted Answer

$$F = 24\ \mathrm{N}$$

Question 16

A 100-N weight is placed a distance $$L_1 to $$the left of a frictionless pin on a massless board. A downward force $$F is $$applied a distance $$L_2 to $$the right. If $$L_2 is $$increased, what happens to the required force $$F to $$keep the board in equilibrium?

Accepted Answer

It decreases.

Question 17

A fixed disk has a string wrapped around it with a hanging mass. The torque about the center is given by $$	au = r F. If $$the disk's diameter is doubled and the mass is kept the same, what happens to the torque?

Accepted Answer

It doubles.

Question 18

Ten identical point masses are arranged in different patterns around an axis. Which arrangement is hardest to start rotating?

Accepted Answer

The one with the most mass farthest from the axis.

Question 19

A student holds a meter stick by one end. A 1,000 g mass is hung at various positions and angles. What factor most affects the difficulty of holding the stick steady?

Accepted Answer

The perpendicular distance from the hand to the mass.

Question 20

A meter stick is held horizontally with a 500 g mass at the 50 cm mark and a 1,000 g mass at the 100 cm mark. In which case does the student need to exert a greater torque: (A) 500 g at 50 cm, 1,000 g at 100 cm, or (B) 1,000 g at 50 cm, 500 g at 100 cm?

Accepted Answer

Case A requires greater torque.

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