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 machinist turns the power on to a grinding wheel,which is at rest at time t = 0.00 s.The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of   The wheel is run at that angular velocity for 37 s and then power is shut off.The wheel decelerates uniformly at   until the wheel stops.In this situation,the time interval of angular deceleration (slowing down)is closest to:

Accepted Answer

A) 17 s 
B) 15 s 
C) 19 s 
D) 21 s 
E) 23 s 
A) 17 s 
B) 15 s 
C) 19 s 
D) 21 s 
E) 23 s

Question 3

A 1.15-kg grinding wheel 22.0 cm in diameter is spinning counterclockwise at a rate of 20.0 revolutions per second.When the power to the grinder is turned off,the grinding wheel slows with constant angular acceleration and takes 80.0 s to come to a rest.
(a)What was the angular acceleration (in rad/s2)of the grinding wheel as it came to rest if we take a counterclockwise rotation as positive?
(b)How many revolutions did the wheel make during the time it was coming to rest?

Accepted Answer

(a)-1.57 r

Question 4

In the figure,the rotor of a gyroscope is a uniform disk that has a radius of 13.8 cm and a moment of inertia about its axis of 4.0 × 10-3 kg ∙ m2.The length of the rotor shaft is 6.9 cm.The ball pivot at P is frictionless.At a given instant,the rotor shaft is horizontal and the rotor is rotating with an angular velocity of 90 rad/s about its axis OP,as shown.The rotor is viewed from point Q on the axis.The precessional linear velocity of point O,including the direction seen from point Q,is closest to

Accepted Answer

A) 0.054 m/s,leftward 
B) 0.054 m/s,upward 
C) 0.054 m/s,rightward 
D) 0.11 m/s,downward 
E) 0.11 m/s,rightward 
A) 0.054 m/s,leftward 
B) 0.054 m/s,upward 
C) 0.054 m/s,rightward 
D) 0.11 m/s,downward 
E) 0.11 m/s,rightward

Question 5

A 72.0-kg person pushes on a small doorknob with a force of 5.00 N perpendicular to the surface of the door.The doorknob is located 0.800 m from axis of the frictionless hinges of the door.The door begins to rotate with an angular acceleration of 2.00 rad/s2.What is the moment of inertia of the door about the hinges?

Accepted Answer

A) 4.28 kg ∙ m2 
B) 7.52 kg ∙ m2 
C) 1.88 kg ∙ m2 
D) 0.684 kg ∙ m2 
E) 2.74 kg ∙ m2 
A) 4.28 kg ∙ m2 
B) 7.52 kg ∙ m2 
C) 1.88 kg ∙ m2 
D) 0.684 kg ∙ m2 
E) 2.74 kg ∙ m2

Question 6

A 500-g particle is located at the point   = 4m   + 3m   - 2m   and is moving with a velocity   = 5 m/s   -2 ms   + 4 m/s   .What is the angular momentum of this particle about the origin?

Accepted Answer

A) (24   - 6   - 8   )kg ∙ m2/s 
B) (12   - 3   - 4   )kg ∙ m2/s 
C) (8   + 14   - 13   )kg ∙ m2/s 
D) (10   -   + 2   )kg ∙ m2/s 
E) (4   - 13   - 11.5   )kg ∙ m2/s 
A) (24   - 6   - 8   )kg ∙ m2/s 
B) (12   - 3   - 4   )kg ∙ m2/s 
C) (8   + 14   - 13   )kg ∙ m2/s 
D) (10   -   + 2   )kg ∙ m2/s 
E) (4   - 13   - 11.5   )kg ∙ m2/s

Question 7

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 8

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 9

A uniform solid 5.25-kg cylinder is released from rest and rolls without slipping down an inclined plane inclined at 18° to the horizontal.How fast is it moving after it has rolled 2.2 m down the plane?

Accepted Answer

A) 4.3 m/s 
B) 5.2 m/s 
C) 3.0 m/s 
D) 3.7 m/s 
E) 2.6 m/s 
A) 4.3 m/s 
B) 5.2 m/s 
C) 3.0 m/s 
D) 3.7 m/s 
E) 2.6 m/s

Question 10

A stepladder consists of two halves,hinged at the top,and connected by a tie rod that keeps the two halves from spreading apart.In this particular instance,the two halves are 2.50 m long,the tie rod is connected to the center of each half and is 70.0 cm long.An 800-N person stands 3/5 of the way up the stepladder,as shown in the figure.Neglecting the weight of the ladder,and assuming that the ladder is resting on a smooth floor,what is the tension in the tie rod? Note: To solve this problem you must "cut" the ladder in half and consider the equilibrium of forces and torques acting on each half of the ladder.

Accepted Answer

A) 140 N 
B) 240 N 
C) 280 N 
D) 360 N 
E) 560 N 
A) 140 N 
B) 240 N 
C) 280 N 
D) 360 N 
E) 560 N

Question 11

A bicycle wheel of radius 0.36 m and mass 3.2 kg is set spinning at 4.00 rev/s.A very light bolt is attached to extend the axle in length,and a string is attached to the axle at a distance of 0.10 m from the wheel.Initially the axle of the spinning wheel is horizontal,and the wheel is suspended only from the string.We can ignore the mass of the axle and spokes.At what rate will the wheel process about the vertical?

Accepted Answer

A) 2.9 rpm 
B) 1.9 rpm 
C) 18 rpm 
D) 0.30 rpm 
E) 0.77 rpm 
A) 2.9 rpm 
B) 1.9 rpm 
C) 18 rpm 
D) 0.30 rpm 
E) 0.77 rpm

Question 12

What is the torque about the origin on a particle located at      = 3 m   + 4 m   - 2 m   if a force   = 5 N   - 2 N   + 3 N   acts on the particle?

Accepted Answer

A) (8   +   - 26   )N ∙ m 
B) (8   - 19   - 26   )N ∙ m 
C) (8   + 2   +   )N ∙ m 
D) (16   - 19   - 26   )N ∙ m 
E) (8   - 2   +   )N ∙ m 
A) (8   +   - 26   )N ∙ m 
B) (8   - 19   - 26   )N ∙ m 
C) (8   + 2   +   )N ∙ m 
D) (16   - 19   - 26   )N ∙ m 
E) (8   - 2   +   )N ∙ m

Question 13

When a rigid body rotates about a fixed axis,all the points in the body have the same

Accepted Answer

A) tangential speed. 
B) angular acceleration. 
C) tangential acceleration. 
D) linear displacement. 
E) centripetal acceleration. 
A) tangential speed. 
B) angular acceleration. 
C) tangential acceleration. 
D) linear displacement. 
E) centripetal acceleration.

Question 14

A light triangular plate OAB is in a horizontal plane.Three forces,     and   act on the plate,which is pivoted about a vertical axes through point O.In the figure,   2 is perpendicular to OB.Consider the counterclockwise sense as positive.The sum of the torques about the vertical axis through point O,acting on the plate due to forces F1,F2,and F3,is closest to

Accepted Answer

A) 4.1 N ∙ m. 
B) 5.4 N ∙ m. 
C) -4.1 N ∙ m. 
D) -5.4 N ∙ m. 
E) zero. 
A) 4.1 N ∙ m. 
B) 5.4 N ∙ m. 
C) -4.1 N ∙ m. 
D) -5.4 N ∙ m. 
E) zero.

Question 15

As you are leaving a building,the door opens outward.If the hinges on the door are on your right,what is the direction of the angular velocity of the door as you open it?

Accepted Answer

A) up 
B) down 
C) to your left 
D) to your right 
E) forwards 
A) up 
B) down 
C) to your left 
D) to your right 
E) forwards

Question 16

A 5.0-m long,12-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 m from the wall.The coefficient of static friction between the floor and the ladder is 0.28.What distance,measured along the ladder from the bottom,can a 60-kg person climb before the ladder starts to slip?

Accepted Answer

A) 4.0 m 
B) 3.7 m 
C) 1.7 m 
D) 1.3 m 
E) 3.3 m 
A) 4.0 m 
B) 3.7 m 
C) 1.7 m 
D) 1.3 m 
E) 3.3 m

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 500-g particle is located at the point = 4m + 3m - 2m and is moving with a velocity = 5 m/s -2 ms + 4 m/s .What is the angular momentum of this particle about the origin?

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?

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 solid 5.25-kg cylinder is released from rest and rolls without slipping down an inclined plane inclined at 18° to the horizontal.How fast is it moving after it has rolled 2.2 m down the plane?

What is the torque about the origin on a particle located at = 3 m + 4 m - 2 m if a force = 5 N - 2 N + 3 N acts on the particle?

When a rigid body rotates about a fixed axis,all the points in the body have the same

As you are leaving a building,the door opens outward.If the hinges on the door are on your right,what is the direction of the angular velocity of the door as you open it?

Concepts of Motion

Kinematics in One Dimension

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Dynamics I: Motion Along a Line

Newtons Third Law

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Newtons Theory of Gravity

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A Macroscopic Description of Matter

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The Micromacro Connection

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