Question 1

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. C

Question 2

What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ?

Accepted Answer

A) -3.00   + 5.00   - 9.00   
B) -5.00   + 2.00   - 6.00   
C) -9.00   - 3.00   - 3.00   
D) -4.00   + 3.00   - 1.00   
E) 2.00   -9.00   - 2.00   
A) -3.00   + 5.00   - 9.00   
B) -5.00   + 2.00   - 6.00   
C) -9.00   - 3.00   - 3.00   
D) -4.00   + 3.00   - 1.00   
E) 2.00   -9.00   - 2.00   A

Question 3

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. D

Question 4

A tire is rolling along a road,without slipping,with a velocity v.A piece of tape is attached to the tire.When the tape is opposite the road (at the top of the tire),its velocity with respect to the road is

Accepted Answer

A) 2v. 
B) v. 
C) 1.5v. 
D) zero. 
E) The velocity depends on the radius of the tire. 
A) 2v. 
B) v. 
C) 1.5v. 
D) zero. 
E) The velocity depends on the radius of the tire.

Question 5

There must be equal amounts of mass on both side of the center of mass of an object.

Accepted Answer

A) True 
 B)False

Question 6

A long thin rod of length L has a linear density λ(x)= Ax where x is the distance from the left end of the rod.
(a)How far is the center of mass of the rod from the left end of the rod?
(b)What is the mass of the rod?

Accepted Answer

The answer of A long thin rod of length L...

Question 7

A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m2.If the arms are pulled in so the moment of inertia decreases to 1.80 kg ∙ m2,what is the final angular speed?

Accepted Answer

A) 2.25 rad/s 
B) 4.60 rad/s 
C) 6.25 rad/s 
D) 1.76 rad/s 
E) 0.810 rad/s 
A) 2.25 rad/s 
B) 4.60 rad/s 
C) 6.25 rad/s 
D) 1.76 rad/s 
E) 0.810 rad/s

Question 8

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 9

A slender uniform rod 100.00 cm long is used as a meter stick.Two parallel axes that are perpendicular to the rod are considered.The first axis passes through the 50-cm mark and the second axis passes through the 30-cm mark.What is the ratio of the moment of inertia through the second axis to the moment of inertia through the first axis?

Accepted Answer

A) I2/I1 = 1.5 
B) I2/I1 = 1.7 
C) I2/I1 = 1.9 
D) I2/I1 = 2.1 
E) I2/I1 = 2.3 
A) I2/I1 = 1.5 
B) I2/I1 = 1.7 
C) I2/I1 = 1.9 
D) I2/I1 = 2.1 
E) I2/I1 = 2.3

Question 10

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 11

The angular acceleration of a wheel is given in   by   where t is in seconds.If the wheel starts from rest at   when is the next time the wheel is at rest?

Accepted Answer

A) 5.1 s 
B) 8.4 s 
C) 6.9 s 
D) 3.6 s 
A) 5.1 s 
B) 8.4 s 
C) 6.9 s 
D) 3.6 s

Question 12

A 2.00-m rod of negligible mass connects two very small objects at its ends.The mass of one object is 1.00 kg and the mass of the other is unknown.The center of mass of this system is on the rod a distance 1.60 m from the 1.00-kg mass object.What is the mass of the other object?

Accepted Answer

A) 4.11 kg 
B) 3.22 kg 
C) 4.00 kg 
D) 0.250 kg 
E) 0.800 kg 
A) 4.11 kg 
B) 3.22 kg 
C) 4.00 kg 
D) 0.250 kg 
E) 0.800 kg

Question 13

An 82.0 kg-diver stands at the edge of a light 5.00-m diving board,which is supported by two narrow pillars 1.60 m apart,as shown in the figure.Find the magnitude and direction of the force exerted on the diving board
(a)by pillar A.
(b)by pillar B.

Accepted Answer

(a)1.71 kN

Question 14

If two vectors are perpendicular to each other,their cross product must be zero.

Accepted Answer

A) True 
 B)False

Question 15

The angular momentum of a system remains constant

Accepted Answer

A) when the total kinetic energy is constant. 
B) when no net external force acts on the system. 
C) when the linear momentum and the energy are constant. 
D) when no torque acts on the system. 
E) all the time since it is a conserved quantity. 
A) when the total kinetic energy is constant. 
B) when no net external force acts on the system. 
C) when the linear momentum and the energy are constant. 
D) when no torque acts on the system. 
E) all the time since it is a conserved quantity.

Question 16

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 17

A 1.25-kg ball begins rolling from rest with constant angular acceleration down a hill.If it takes 3.60 s for it to make the first complete revolution,how long will it take to make the next complete revolution?

Accepted Answer

The answer of A 1.25-kg ball begins rolling from rest...

Question 18

A 1.10-kg wrench is acting on a nut trying to turn it.The length of the wrench lies directly to the east of the nut.A force 150.0 N acts on the wrench at a position 15.0 cm from the center of the nut in a direction 30.0° north of east.What is the magnitude of the torque about the center of the nut?

Accepted Answer

A) 22.5 N ∙ m 
B) 11.3 N ∙ m 
C) 19.5 N ∙ m 
D) 2250 N ∙ m 
E) 1949 N ∙ m 
A) 22.5 N ∙ m 
B) 11.3 N ∙ m 
C) 19.5 N ∙ m 
D) 2250 N ∙ m 
E) 1949 N ∙ m

Question 19

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii and are of uniform density.If the three are released simultaneously at the top of an inclined plane and roll without slipping,which one will reach the bottom first?

Accepted Answer

A) solid sphere 
B) hollow pipe 
C) solid cylinder 
D) They all reach the bottom at the same time. 
A) solid sphere 
B) hollow pipe 
C) solid cylinder 
D) They all reach the bottom at the same time.

Question 20

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

Accepted Answer

A) 16,directed into the plane 
B) 16,directed out of the plane 
C) 45,directed on the plane 
D) 45,directed into the plane 
E) 45,directed out of the plane 
A) 16,directed into the plane 
B) 16,directed out of the plane 
C) 45,directed on the plane 
D) 45,directed into the plane 
E) 45,directed out of the plane

Exam 12: Rotation of a Rigid Body

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

What is the vector product of = 2.00 + 3.00 + 1.00 and = 1.00 - 3.00 - 2.00 ?

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 tire is rolling along a road,without slipping,with a velocity v.A piece of tape is attached to the tire.When the tape is opposite the road (at the top of the tire),its velocity with respect to the road is

There must be equal amounts of mass on both side of the center of mass of an object.

A long thin rod of length L has a linear density λ(x)= Ax where x is the distance from the left end of the rod. (a)How far is the center of mass of the rod from the left end of the rod? (b)What is the mass of the rod?

A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m2.If the arms are pulled in so the moment of inertia decreases to 1.80 kg ∙ m2,what is the final angular speed?

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?

The angular acceleration of a wheel is given in by where t is in seconds.If the wheel starts from rest at when is the next time the wheel is at rest?

A 2.00-m rod of negligible mass connects two very small objects at its ends.The mass of one object is 1.00 kg and the mass of the other is unknown.The center of mass of this system is on the rod a distance 1.60 m from the 1.00-kg mass object.What is the mass of the other object?

An 82.0 kg-diver stands at the edge of a light 5.00-m diving board,which is supported by two narrow pillars 1.60 m apart,as shown in the figure.Find the magnitude and direction of the force exerted on the diving board (a)by pillar A. (b)by pillar B.

If two vectors are perpendicular to each other,their cross product must be zero.

The angular momentum of a system remains constant

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?

A 1.25-kg ball begins rolling from rest with constant angular acceleration down a hill.If it takes 3.60 s for it to make the first complete revolution,how long will it take to make the next complete revolution?

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii and are of uniform density.If the three are released simultaneously at the top of an inclined plane and roll without slipping,which one will reach the bottom first?

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

Concepts of Motion

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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 figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m².If the arms are pulled in so the moment of inertia decreases to 1.80 kg ∙ m²,what is the final angular speed?