Question 1

Which of the following statements about the motion of the second hand of a clock is true?

Accepted Answer

A) The tangential velocity of the tip is constant. 
B) The angular velocity is zero. 
C) The angular acceleration is zero. 
D) The radial acceleration is zero. 
E) The tangential acceleration is nonzero. 
A) The tangential velocity of the tip is constant. 
B) The angular velocity is zero. 
C) The angular acceleration is zero. 
D) The radial acceleration is zero. 
E) The tangential acceleration is nonzero.

Question 2

The Crab Pulsar rotates 30 times per second.However,its period is increasing by about 10-5 s per year.How many years will it take before its period of rotation has doubled?

Accepted Answer

A) 3.0 $\times$ 106 yr 
B) 6.7 $\times$ 103 yr 
C) 3.3 $\times$ 103 yr 
D) 1.05 $\times$ 1010 yr 
E) 2.10 $\times$ 1010 yr 
A) 3.0 $\times$ 106 yr 
B) 6.7 $\times$ 103 yr 
C) 3.3 $\times$ 103 yr 
D) 1.05 $\times$ 1010 yr 
E) 2.10 $\times$ 1010 yr

Question 3

The moment of inertia of a certain cylinder,whose mass is not distributed uniformly,is 0.6mR2 about its geometric axis.The translational speed of the center of mass after it starts from rest and rolls 14 m down a 30º incline is approximately

Accepted Answer

A) 9.3 m/s 
B) 86 m/s 
C) 13 m/s 
D) 3.1 m/s 
E) 41 m/s 
A) 9.3 m/s 
B) 86 m/s 
C) 13 m/s 
D) 3.1 m/s 
E) 41 m/s

Question 4

A disc-shaped grindstone of mass 3.0 kg and radius 8.0 cm is spinning at 600 rev/min.After the power is shut off,a man continues to sharpen his axe by holding it against the grindstone until it stops 10 s later.What is the average torque exerted by the axe on the grindstone?

Accepted Answer

A) 9.6 mN · m 
B) 0.12 N · m 
C) 0.75 N · m 
D) 0.60 kN · m 
E) 0.060 N · m 
A) 9.6 mN · m 
B) 0.12 N · m 
C) 0.75 N · m 
D) 0.60 kN · m 
E) 0.060 N · m

Question 5

The angular acceleration of the flywheel of a generator is given by   where b and c are constants and $\alpha$ is in rad/s2 provided t is in seconds.If the initial angular velocity is taken to be $\omega$0,the angular velocity at time t is given by

Accepted Answer

A) $\omega$0 + 6bt2 - 12ct3  
B) 6b - 24ct 
C) 3bt2 - 4ct3 + $\omega$0  
D) 3bt2 - 4ct3  
E) 6b - 24ct + $\omega$0  
A) $\omega$0 + 6bt2 - 12ct3  
B) 6b - 24ct 
C) 3bt2 - 4ct3 + $\omega$0  
D) 3bt2 - 4ct3  
E) 6b - 24ct + $\omega$0

Question 6

-A 2.0-kg mass is attached to the end of a 5.0-m rope.The mass moves in a circular path on a horizontal frictionless surface.If the breaking strength of the rope is 40 N,the maximum translational speed with which you can swing the mass without breaking the rope is approximately

Accepted Answer

A) 3.2 m/s 
B) 4.0 m/s 
C) 10 m/s 
D) 20 m/s 
E) 0.20 km/s 
A) 3.2 m/s 
B) 4.0 m/s 
C) 10 m/s 
D) 20 m/s 
E) 0.20 km/s

Question 7

A penny is placed 0.10 m from the center of a turntable.If the coefficient of static friction between the penny and the turntable is 0.50,the maximum linear speed at which the penny can travel without slipping is approximately

Accepted Answer

A) 0.49 m/s 
B) 0.70 m/s 
C) 1.3 m/s 
D) 1.4 m/s 
E) 0.20 km/s 
A) 0.49 m/s 
B) 0.70 m/s 
C) 1.3 m/s 
D) 1.4 m/s 
E) 0.20 km/s

Question 8

A spherically symmetric object with mass m = 0.2 kg and radius r = 10 cm,rolls without slipping on a horizontal surface with speed 1 m/s.It then rolls up an incline that is at an angle 30S1U1P1$\circ$S1S1P0 with the horizon and comes to rest at a distance of 0.6 m along the incline.What is the moment of inertia of the object about an axis through the center of mass?

Accepted Answer

A) 1.0 $\times$ 10-4 kg · m2/s 
B) 2.0 $\times$ 10-3 kg · m2/s 
C) 9.8 $\times$ 10-3 kg · m2/s 
D) 1.2 $\times$ 10-2 kg · m2/s 
E) 8.0 $\times$ 10-4 kg · m2/s 
A) 1.0 $\times$ 10-4 kg · m2/s 
B) 2.0 $\times$ 10-3 kg · m2/s 
C) 9.8 $\times$ 10-3 kg · m2/s 
D) 1.2 $\times$ 10-2 kg · m2/s 
E) 8.0 $\times$ 10-4 kg · m2/s

Question 9

A uniform cylinder (I =   mR2)of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane.The acceleration of the cylinder down the plane is approximately

Accepted Answer

A) 2.0 m/s2  
B) 3.9 m/s2  
C) 4.9 m/s2  
D) 5.8 m/s2  
E) 9.8 m/s2  
A) 2.0 m/s2  
B) 3.9 m/s2  
C) 4.9 m/s2  
D) 5.8 m/s2  
E) 9.8 m/s2

Question 10

Two objects,m1 and m2,both of mass m,are placed on a horizontal platform which is rotating at a constant angular velocity.m1 is located at a distance   R from the axis of rotation and m2 is located at a R.The tangential acceleration of mass m1 ____ to the tangential acceleration of m2.

Accepted Answer

A) is less than 
B) is equal to 
C) is greater than 
D) depends how fast it is rotating 
E) unable to tell 
A) is less than 
B) is equal to 
C) is greater than 
D) depends how fast it is rotating 
E) unable to tell

Question 11

A disk with a radius of 1.5 m whose moment of inertia is 34 kg · m2 is caused to rotate by a force of 160 N tangent to the circumference.The angular acceleration of the disk is approximately

Accepted Answer

A) 0.14 rad/s2  
B) 0.23 rad/s2  
C) 4.4 rad/s2  
D) 7.1 rad/s2  
E) 23 rad/s2  
A) 0.14 rad/s2  
B) 0.23 rad/s2  
C) 4.4 rad/s2  
D) 7.1 rad/s2  
E) 23 rad/s2

Question 12

A stone of mass 10 kg has a rotational inertia of 2.4 kg · m2 about an axis A parallel to an axis through the center of mass.If axis A is 0.20m from the center of mass axis,the rotational inertia about the center of mass axis is

Accepted Answer

A) 0.40 kg · m2  
B) 2.0 kg · m2  
C) 2.4 kg · m2  
D) 2.8 kg · m2  
E) 4.4 kg · m2  
A) 0.40 kg · m2  
B) 2.0 kg · m2  
C) 2.4 kg · m2  
D) 2.8 kg · m2  
E) 4.4 kg · m2

Question 13

The amount of work done on a rotating body can be expressed in terms of the product of

Accepted Answer

A) force and lever arm. 
B) torque and angular velocity. 
C) torque and angular acceleration. 
D) force and time of application of the force. 
E) torque and angular displacement. 
A) force and lever arm. 
B) torque and angular velocity. 
C) torque and angular acceleration. 
D) force and time of application of the force. 
E) torque and angular displacement.

Question 14

A body that moves with a constant speed in a circle

Accepted Answer

A) experiences no acceleration. 
B) undergoes no change in velocity. 
C) has no resultant force acting on it. 
D) has no work done on it. 
E) is described by all of these. 
A) experiences no acceleration. 
B) undergoes no change in velocity. 
C) has no resultant force acting on it. 
D) has no work done on it. 
E) is described by all of these.

Question 15

For a disc of mass M and radius R that is rolling without slipping,which is greater,its translational or its rotational kinetic energy?

Accepted Answer

A) Its translational kinetic energy is greater. 
B) Its rotational kinetic energy is greater. 
C) They are equal. 
D) The answer depends on the radius. 
E) The answer depends on the mass. 
A) Its translational kinetic energy is greater. 
B) Its rotational kinetic energy is greater. 
C) They are equal. 
D) The answer depends on the radius. 
E) The answer depends on the mass.

Question 16

A thin solid disk of radius R = 0.5 m and mass M = 2.0 kg is rolling without slipping on a horizontal surface with a linear speed v = 5.0 m/s.The disk now rolls without slipping up an inclined plane that is at an angle of 60 degrees to the vertical.Calculate the maximum height that the disk rolls up the incline.

Accepted Answer

A) 5.1 m 
B) 2.6 m 
C) 2.9 m 
D) 3.1 m 
E) 1.3 m 
A) 5.1 m 
B) 2.6 m 
C) 2.9 m 
D) 3.1 m 
E) 1.3 m

Question 17

The moment of inertia of a set of dumbbells,considered as two mass points m separated by a distance 2L about the axis AA,is

Accepted Answer

A) mL2  
B)    mL2  
C) 2mL2  
D)    mL2  
E) 4mL2  
A) mL2  
B)    mL2  
C) 2mL2  
D)    mL2  
E) 4mL2

Question 18

Torque is defined as

Accepted Answer

A) a force tending to cause rotation. 
B) the cross product of force and displacement. 
C) the product of the force and the angular displacement. 
D) the product of the force and the angular velocity. 
E) the rotational work done. 
A) a force tending to cause rotation. 
B) the cross product of force and displacement. 
C) the product of the force and the angular displacement. 
D) the product of the force and the angular velocity. 
E) the rotational work done.

Question 19

A turntable rotating at 8.0 rad/s slows to a stop in 10 s.If the acceleration is constant,the angle through which the turntable rotates in the 10 s is

Accepted Answer

A) 0.80 rad 
B) 0.40 rad 
C) 40 rad 
D) 80 rad 
E) 16 rad 
A) 0.80 rad 
B) 0.40 rad 
C) 40 rad 
D) 80 rad 
E) 16 rad

Question 20

Assume that all of the mass of a bicycle wheel is concentrated at its rim.Such a wheel of mass 1.2 kg and radius 30 cm starts from rest at the top of a hill 100 m long and inclined at 20º to the horizontal.What will be the speed of the wheel at the bottom of the hill if it rolls without slipping?

Accepted Answer

A) 21 m/s 
B) 26 m/s 
C) 15 m/s 
D) 33 m/s 
E) 37 m/s 
A) 21 m/s 
B) 26 m/s 
C) 15 m/s 
D) 33 m/s 
E) 37 m/s

Exam 9: Rotation

Which of the following statements about the motion of the second hand of a clock is true?

The Crab Pulsar rotates 30 times per second.However,its period is increasing by about 10-5 s per year.How many years will it take before its period of rotation has doubled?

The moment of inertia of a certain cylinder,whose mass is not distributed uniformly,is 0.6mR2 about its geometric axis.The translational speed of the center of mass after it starts from rest and rolls 14 m down a 30º incline is approximately

A disc-shaped grindstone of mass 3.0 kg and radius 8.0 cm is spinning at 600 rev/min.After the power is shut off,a man continues to sharpen his axe by holding it against the grindstone until it stops 10 s later.What is the average torque exerted by the axe on the grindstone?

The angular acceleration of the flywheel of a generator is given by where b and c are constants and α\alphaα is in rad/s2 provided t is in seconds.If the initial angular velocity is taken to be ω\omegaω 0,the angular velocity at time t is given by

-A 2.0-kg mass is attached to the end of a 5.0-m rope.The mass moves in a circular path on a horizontal frictionless surface.If the breaking strength of the rope is 40 N,the maximum translational speed with which you can swing the mass without breaking the rope is approximately

A penny is placed 0.10 m from the center of a turntable.If the coefficient of static friction between the penny and the turntable is 0.50,the maximum linear speed at which the penny can travel without slipping is approximately

A uniform cylinder (I = mR2)of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane.The acceleration of the cylinder down the plane is approximately

Two objects,m1 and m2,both of mass m,are placed on a horizontal platform which is rotating at a constant angular velocity.m1 is located at a distance R from the axis of rotation and m2 is located at a R.The tangential acceleration of mass m1 ____ to the tangential acceleration of m2.

A disk with a radius of 1.5 m whose moment of inertia is 34 kg · m2 is caused to rotate by a force of 160 N tangent to the circumference.The angular acceleration of the disk is approximately

A stone of mass 10 kg has a rotational inertia of 2.4 kg · m2 about an axis A parallel to an axis through the center of mass.If axis A is 0.20m from the center of mass axis,the rotational inertia about the center of mass axis is

The amount of work done on a rotating body can be expressed in terms of the product of

A body that moves with a constant speed in a circle

For a disc of mass M and radius R that is rolling without slipping,which is greater,its translational or its rotational kinetic energy?

The moment of inertia of a set of dumbbells,considered as two mass points m separated by a distance 2L about the axis AA,is

Torque is defined as

A turntable rotating at 8.0 rad/s slows to a stop in 10 s.If the acceleration is constant,the angle through which the turntable rotates in the 10 s is

Assume that all of the mass of a bicycle wheel is concentrated at its rim.Such a wheel of mass 1.2 kg and radius 30 cm starts from rest at the top of a hill 100 m long and inclined at 20º to the horizontal.What will be the speed of the wheel at the bottom of the hill if it rolls without slipping?

Systems of Measurement

Motion in One Dimension

Motion in Two and Three Dimensions

Newtons Laws

Applications of Newtons Laws

Work and Energy

Conservation of Energy

Systems of Particles and Conservation of Linear Momentum

Conservation of Angular Momentum

Gravity

Static Equilibrium and Elasticity

Fluids

Oscillations

Wave Motion

Superposition and Standing Waves

Temperature and the Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

The Second Law of Thermodynamics

Thermal Properties and Processes

The Electric Field I: Discrete Charge Distributions

The Electric Field Ii: Continuous Charge Distributions

Electric Potential

Capacitance

Electric Current and Direct-Current Circuits

The Magnetic Field

Sources of the Magnetic Field

Magnetic Induction

Alternating-Current Circuits

Maxwells Equations and Electromagnetic Waves

Properties of Light

Optical Images

Interference and Diffraction

Wave Particle Duality and Quantum Physics

Applications of the Schrodinger Equation

Atoms

Molecules

Solids and the Theory of Conduction

Relativity

Nuclear Physics

Elementary Particles and the Beginning of the Universe

Filters

The Crab Pulsar rotates 30 times per second.However,its period is increasing by about 10^-5 s per year.How many years will it take before its period of rotation has doubled?

The moment of inertia of a certain cylinder,whose mass is not distributed uniformly,is 0.6mR² about its geometric axis.The translational speed of the center of mass after it starts from rest and rolls 14 m down a 30º incline is approximately

A uniform cylinder (I = mR²)of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane.The acceleration of the cylinder down the plane is approximately

Two objects,m₁ and m₂,both of mass m,are placed on a horizontal platform which is rotating at a constant angular velocity.m₁ is located at a distance R from the axis of rotation and m₂ is located at a R.The tangential acceleration of mass m₁ ____ to the tangential acceleration of m₂.

A disk with a radius of 1.5 m whose moment of inertia is 34 kg · m² is caused to rotate by a force of 160 N tangent to the circumference.The angular acceleration of the disk is approximately

A stone of mass 10 kg has a rotational inertia of 2.4 kg · m² about an axis A parallel to an axis through the center of mass.If axis A is 0.20m from the center of mass axis,the rotational inertia about the center of mass axis is