Question 1

What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?

Accepted Answer

A)  6.93 
B)  -6.93 
C)  4.00 
D)  -4.00 
E)  8.00 
A)  6.93 
B)  -6.93 
C)  4.00 
D)  -4.00 
E)  8.00

Question 2

A wheel has a radius of 0.40 m and is mounted on frictionless bearings. A block is suspended from a rope that is wound on the wheel and attached to it (see figure). The wheel is released from rest and the block descends 1.5 m in 2.00 s without any slipping of the rope. The tension in the rope during the descent of the block is 20 N. What is the moment of inertia of the wheel?

Accepted Answer

A)  3.5 kg · m2 
B)  3.7 kg · m2 
C)  3.9 kg · m2 
D)  4.1 kg · m2 
E)  4.3 kg · m2 
A)  3.5 kg · m2 
B)  3.7 kg · m2 
C)  3.9 kg · m2 
D)  4.1 kg · m2 
E)  4.3 kg · m2

Question 3

In the figure, a uniform rectangular crate 0.40 m wide and 1.0 m tall rests on a horizontal surface. The crate weighs 930 N, and its center of gravity is at its geometric center. A horizontal force F is applied at a distance h above the floor. If h = 0.61 m, what minimum value of F is required to make the crate start to tip over? Static friction is large enough that the crate does not start to slide.

Accepted Answer

The answer of In the figure, a uniform rectangular crate...

Question 4

A string is wrapped around a pulley with a radius of 2.0 cm and no appreciable friction in its axle. The pulley is initially not turning. A constant force of 50 N is applied to the string, which does not slip, causing the pulley to rotate and the string to unwind. If the string unwinds 1.2 m in 4.9 s, what is the moment of inertia of the pulley?

Accepted Answer

A)  0.17 kg∙m2 
B)  17 kg∙m2 
C)  14 kg∙m2 
D)  0.20 kg∙m2 
E)  0.017 kg∙m2 
A)  0.17 kg∙m2 
B)  17 kg∙m2 
C)  14 kg∙m2 
D)  0.20 kg∙m2 
E)  0.017 kg∙m2

Question 5

A solid, uniform sphere of mass 2.0 kg and radius 1.7 m rolls from rest without slipping down an inclined plane of height 7.0 m. What is the angular velocity of the sphere at the bottom of the inclined plane?

Accepted Answer

A)  5.8 rad/s 
B)  9.9 rad/s 
C)  11 rad/s 
D)  7.0 rad/s 
A)  5.8 rad/s 
B)  9.9 rad/s 
C)  11 rad/s 
D)  7.0 rad/s

Question 6

If an irregularly shaped object (such as a wrench) is dropped from rest in a classroom and feels no air resistance, it will

Accepted Answer

A)  accelerate but will not spin. 
B)  accelerate and turn until its center of gravity reaches its lowest point. 
C)  accelerate and turn about its center of gravity with uniform angular speed. 
D)  accelerate and turn about its center of gravity with uniform angular acceleration. 
E)  accelerate and spin until its center of gravity reaches its highest point. 
A)  accelerate but will not spin. 
B)  accelerate and turn until its center of gravity reaches its lowest point. 
C)  accelerate and turn about its center of gravity with uniform angular speed. 
D)  accelerate and turn about its center of gravity with uniform angular acceleration. 
E)  accelerate and spin until its center of gravity reaches its highest point.

Question 7

A uniform hollow spherical ball of mass 1.75 kg and radius 40.0 cm rolls without slipping up a ramp that rises at 30.0° above the horizontal. The speed of the ball at the base of the ramp is 2.63 m/s. While the ball is moving up the ramp, find
(a) the acceleration (magnitude and direction) of its center of mass and
(b) the friction force (magnitude and direction) acting on it due to the surface of the ramp.

Accepted Answer

(a) 2.94 m/s² down th

Question 8

A bicycle is traveling north at 5.0 m/s. The mass of the wheel, 2.0 kg, is uniformly distributed along the rim, which has a radius of 20 cm. What are the magnitude and direction of the angular momentum of the wheel about its axle?

Accepted Answer

A)  2.0 kg∙m2/s towards the west 
B)  5.0 kg∙m2/s vertically upwards 
C)  2.0 kg∙m2/s towards the east 
D)  5.0 kg∙m2/s towards the east 
E)  5.0 kg∙m2/s towards the west 
A)  2.0 kg∙m2/s towards the west 
B)  5.0 kg∙m2/s vertically upwards 
C)  2.0 kg∙m2/s towards the east 
D)  5.0 kg∙m2/s towards the east 
E)  5.0 kg∙m2/s towards the west

Question 9

A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg∙m2 is rotating freely with an angular speed of 1.0 rad/s. Two people, each having a mass of 60 kg, are standing right outside the edge of the merry-go-round and step on it with negligible speed. What is the angular speed of the merry-go-round right after the two people have stepped on?

Accepted Answer

A)  0.20 rad/s 
B)  0.40 rad/s 
C)  0.60 rad/s 
D)  0.80 rad/s 
E)  0.67 rad/s 
A)  0.20 rad/s 
B)  0.40 rad/s 
C)  0.60 rad/s 
D)  0.80 rad/s 
E)  0.67 rad/s

Question 10

In the figure, point P is at rest when it is on the x-axis. The linear speed of point P when it reaches the y-axis is closest to

Accepted Answer

A)  0.18 m/s. 
B)  0.24 m/s. 
C)  0.35 m/s. 
D)  0.49 m/s. 
E)  0.71 m/s. 
A)  0.18 m/s. 
B)  0.24 m/s. 
C)  0.35 m/s. 
D)  0.49 m/s. 
E)  0.71 m/s.

Question 11

A 4.50-kg wheel that is 34.5 cm in diameter rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel?

Accepted Answer

A)  0.616 rad/s2 
B)  5.45 rad/s2 
C)  111 rad/s2 
D)  22.5 rad/s2 
E)  10.9 rad/s2 
A)  0.616 rad/s2 
B)  5.45 rad/s2 
C)  111 rad/s2 
D)  22.5 rad/s2 
E)  10.9 rad/s2

Question 12

If   and  
Are nonzero vectors for which  
∙  
= 0, it must follow that

Accepted Answer

A)    ×   = 0. 
B)    is parallel to   . 
C)  |   ×   | = AB. 
D)  |   ×   | = 1. 
A)    ×   = 0. 
B)    is parallel to   . 
C)  |   ×   | = AB. 
D)  |   ×   | = 1.

Question 13

In the figure, point P is at rest when it is on the x-axis. The time t, when P returns to the original position on the x-axis, is closest to

Accepted Answer

A)  13 s. 
B)  18 s. 
C)  25 s. 
D)  35 s. 
E)  50 s. 
A)  13 s. 
B)  18 s. 
C)  25 s. 
D)  35 s. 
E)  50 s.

Question 14

A thin cylindrical shell is released from rest and rolls without slipping down an inclined ramp that makes an angle of 30° with the horizontal. How long does it take it to travel the first 3.1 m?

Accepted Answer

A)  1.4 s 
B)  1.1 s 
C)  2.1 s 
D)  1.6 s 
E)  1.8 s 
A)  1.4 s 
B)  1.1 s 
C)  2.1 s 
D)  1.6 s 
E)  1.8 s

Question 15

In the figure, two blocks, of masses 2.00 kg and 3.00 kg, are connected by a light string that passes over a frictionless pulley of moment of inertia 0.00400 kg · m2 and radius 5.00 cm. The coefficient of friction for the tabletop is 0.300. The blocks are released from rest. Using energy methods, find the speed of the upper block just as it has moved 0.600 m.

Accepted Answer

A)  1.22 m/s 
B)  5.44 m/s 
C)  3.19 m/s 
D)  1.95 m/s 
E)  1.40 m/s 
A)  1.22 m/s 
B)  5.44 m/s 
C)  3.19 m/s 
D)  1.95 m/s 
E)  1.40 m/s

Question 16

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0° above the horizontal. After it has rolled 4.20 m along the ramp, what is the magnitude of the linear acceleration of its center of mass?

Accepted Answer

A)  9.80 m/s2 
B)  4.60 m/s2 
C)  3.29 m/s2 
D)  3.07 m/s2 
E)  2.30 m/s2 
A)  9.80 m/s2 
B)  4.60 m/s2 
C)  3.29 m/s2 
D)  3.07 m/s2 
E)  2.30 m/s2

Question 17

In the figure, four point masses are placed as shown. The x and y coordinates of the center of mass are closest to

Accepted Answer

A)  (2.2 m, 2.6 m). 
B)  (2.2 m, 2.7 m). 
C)  (2.3 m, 2.6 m). 
D)  (2.3 m, 2.7 m). 
E)  (2.3 m, 2.8 m). 
A)  (2.2 m, 2.6 m). 
B)  (2.2 m, 2.7 m). 
C)  (2.3 m, 2.6 m). 
D)  (2.3 m, 2.7 m). 
E)  (2.3 m, 2.8 m).

Question 18

A force   = 3.00 N  
- 2.00 N  
Acts at a location  
= 1.00 m  
+ 2.00 m  
On an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?

Accepted Answer

A)  -1.00 N∙m   
B)  7.00 N∙m   
C)  -3.00 N∙m   
D)  5.00 N∙m   
E)  -8.00 N∙m   
A)  -1.00 N∙m   
B)  7.00 N∙m   
C)  -3.00 N∙m   
D)  5.00 N∙m   
E)  -8.00 N∙m

Question 19

A uniform disk, a uniform hoop, and a uniform solid sphere are released at the same time at the top of an inclined ramp. They all roll without slipping. In what order do they reach the bottom of the ramp?

Accepted Answer

A)  disk, hoop, sphere 
B)  hoop, sphere, disk 
C)  sphere, disk, hoop 
D)  sphere, hoop, disk 
E)  hoop, disk, sphere 
A)  disk, hoop, sphere 
B)  hoop, sphere, disk 
C)  sphere, disk, hoop 
D)  sphere, hoop, disk 
E)  hoop, disk, sphere

Question 20

For the vectors shown in the figure, find the magnitude and direction of   ×  
, assuming that the quantities shown are accurate to two significant figures.

Accepted Answer

A)  26, directed into the plane 
B)  26, directed out of the plane 
C)  31, directed on the plane 
D)  31, directed into the plane 
E)  31, directed out of the plane 
A)  26, directed into the plane 
B)  26, directed out of the plane 
C)  31, directed on the plane 
D)  31, directed into the plane 
E)  31, directed out of the plane

Exam 12: Rotation of a Rigid Body

What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?

A solid, uniform sphere of mass 2.0 kg and radius 1.7 m rolls from rest without slipping down an inclined plane of height 7.0 m. What is the angular velocity of the sphere at the bottom of the inclined plane?

If an irregularly shaped object (such as a wrench) is dropped from rest in a classroom and feels no air resistance, it will

A bicycle is traveling north at 5.0 m/s. The mass of the wheel, 2.0 kg, is uniformly distributed along the rim, which has a radius of 20 cm. What are the magnitude and direction of the angular momentum of the wheel about its axle?

In the figure, point P is at rest when it is on the x-axis. The linear speed of point P when it reaches the y-axis is closest to

A 4.50-kg wheel that is 34.5 cm in diameter rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel?

If and Are nonzero vectors for which ∙ = 0, it must follow that

In the figure, point P is at rest when it is on the x-axis. The time t, when P returns to the original position on the x-axis, is closest to

A thin cylindrical shell is released from rest and rolls without slipping down an inclined ramp that makes an angle of 30° with the horizontal. How long does it take it to travel the first 3.1 m?

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0° above the horizontal. After it has rolled 4.20 m along the ramp, what is the magnitude of the linear acceleration of its center of mass?

In the figure, four point masses are placed as shown. The x and y coordinates of the center of mass are closest to

A force = 3.00 N - 2.00 N Acts at a location = 1.00 m + 2.00 m On an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?

A uniform disk, a uniform hoop, and a uniform solid sphere are released at the same time at the top of an inclined ramp. They all roll without slipping. In what order do they reach the bottom of the ramp?

For the vectors shown in the figure, find the magnitude and direction of × , assuming that the quantities shown are accurate to two significant figures.

Concepts of Motion

Kinematics in One Dimension

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Force and Motion

Dynamics I: Motion Along a Line

Newtons Third Law

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Impulse and Momentum

Energy

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Newtons Theory of Gravity

Oscillations

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A Macroscopic Description of Matter

Work, Heat, and the First Law of Thermodynamics

The Micromacro Connection

Heat Engines and Refrigerators

Traveling Waves

Superpositions

Wave Optics

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Optical Instruments

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Gausss Law

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Potential and Field

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