Question 1

A point P is at a distance R from the axis of rotation of a rigid body. The linear speed, centripetal acceleration, and tangential acceleration of the point can be expressed as

Accepted Answer

The answer of A point P is at a distance...

Question 2

The data used to construct the graph were taken from the tachometer of an airplane. The angular acceleration during the 10 s interval was

Accepted Answer

A)  3.0 rad/s2  
B)  6.0 rad/s2  
C)  8.0 rad/s2  
D)  20 rad/s2  
E)  38 rad/s2

Question 3

A uniform cylinder (I =  mR2) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane. The gain in translational kinetic energy of the cylinder when it has rolled 5 m down the incline of the plane is approximately

Accepted Answer

A)  24 J 
B)  0.12 kJ 
C)  0.24 kJ 
D)  0.35 kJ 
E)  0.59 kJ

Question 4

A solid cylinder, a hollow cylinder, and a square block of equal masses are released at the top of an inclined plane. The cylinders roll down and the block slides down, all with negligible frictional losses. In what order will they arrive at the bottom?

Accepted Answer

A)  solid cylinder, hollow cylinder, block 
B)  hollow cylinder, solid cylinder, block 
C)  block, hollow cylinder, solid cylinder 
D)  block, solid cylinder, hollow cylinder 
E)  all at the same instant

Question 5

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

Question 6

You have a friend who lives in the southern part of the United States, and you live in the northern part. As Earth rotates, your linear velocity is ___________ hers, and your angular velocity is ____________ hers.

Accepted Answer

A)  greater than; equal to 
B)  equal to; greater than 
C)  greater than; less than 
D)  less than; greater than 
E)  less than; equal to

Question 7

A cord attached to a 3.63-kg mass is wrapped around a wheel of radius 0.610 m and released. The moment of inertia of the wheel is 2.71 kg · m2. If the wheel rotates on frictionless bearings, the acceleration of the falling weight is

Accepted Answer

A)  3.26 m/s2  
B)  1.04 m/s2  
C)  2.44 m/s2  
D)  1.95 m/s2  
E)  4.27 m/s2

Question 8

The information on a compact disc is scanned by a laser initially at a radius of 2.4 cm and then out to a maximum of 6.0 cm. Because the dimensions of the pit information remains constant with radius the disk motor adjusts so that the tangential velocity remains a constant. What is the ratio of the inner to outer rotational frequencies?

Accepted Answer

A)  0.16 
B)  6.3 
C)  1.0 
D)  2.5 
E)  0.40

Question 9

You are pedaling a bicycle at 9.8 m/s. The radius of the wheels of the bicycle is 51.9cm. The angular velocity of rotation of the wheels is

Accepted Answer

A)  19 rad/s 
B)  2.5 rad/s 
C)  4.5 rad/s 
D)  3.0 rad/s 
E)  6.3 rad/s

Question 10

In the figure, the rotational inertia of the wheel and axle about the center is
12.0 kg · m2, the constant force F is 39.2 N, and the radius r is 0.800 m. The wheel starts from rest. When the force has acted through 2.00 m, the rotational velocity $\omega$ acquired by the wheel due to this force will be

Accepted Answer

A)  1.26 rad/s 
B)  3.33 rad/s 
C)  3.61 rad/s 
D)  6.24 rad/s 
E)  10.3 rad/s

Question 11

You give an orbiting satellite a command to rotate through an angle given by
$\theta$ = at + bt2 - ct4
Where a, b, and c are constants and $\theta$ is in radians if t is in seconds. What is the angular acceleration of this satellite at time t?

Accepted Answer

A)  at 
B)  a + b - c 
C)  -12 
D)  2b - 12ct2  
E)  zero

Question 12

The ball shown in the figure will loop-the-loop if it starts from a point high enough on the incline. When the ball is at point A, the centripetal force on it is best represented by which of the following vectors?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

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

Question 14

A record turntable rotates through 5.0 rad in 2.8 s as it is accelerated uniformly from rest. What is the angular velocity at the end of that time?

Accepted Answer

A)  0.60 rad/s 
B)  0.90 rad/s 
C)  1.8 rad/s 
D)  3.6 rad/s 
E)  14 rad/s

Question 15

In a laboratory experiment, various torques are applied to a rotor and the angular acceleration is measured. The results are plotted on the accompanying graph. From the graph, the moment of inertia of the rotor is

Accepted Answer

A)  0.010 kg · m2  
B)  0.011 kg · m2  
C)  0.0125 kg · m2  
D)  0.0138 kg · m2  
E)  0.0225 kg · m2

Question 16

A solid disk (I =  MR2) that is 10 cm in diameter has a mass of 4 kg. The force applied at the outer surface required to produce an angular acceleration of 6 rad/s2 about an axis through the center of the disc is

Accepted Answer

A)  0.24 kN 
B)  0.12 kN 
C)  0.30 N 
D)  0.60 N 
E)  1.2 N

Question 17

A uniform disk (Io = ½ mR2) of mass m and radius R is suspended from a point on its rim. The moment of inertia of the disk about an axis perpendicular to the disk through the pivot point is

Accepted Answer

A)  ½ mR2  
B)  mR2  
C)  1.5mR2  
D)  2mR2  
E)  2mR2/3

Question 18

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

Question 19

A spherical shell and a solid sphere (both of the same total mass) are rotating about a diameter at the same angular frequency and with the same rotational kinetic energy. What is the ratio of the spherical shell radius to the solid sphere (i.e., Rspherical shell/Rsolid sphere)?

Accepted Answer

A)  (2/5)1/2  
B)  (3/10)1/2  
C)  (1/2)1/2  
D)  (3/5)1/2  
E)  (2/3)1/2

Exam 9: Rotation

A point P is at a distance R from the axis of rotation of a rigid body. The linear speed, centripetal acceleration, and tangential acceleration of the point can be expressed as

The data used to construct the graph were taken from the tachometer of an airplane. The angular acceleration during the 10 s interval was

A uniform cylinder (I = mR²) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane. The gain in translational kinetic energy of the cylinder when it has rolled 5 m down the incline of the plane is approximately

A solid cylinder, a hollow cylinder, and a square block of equal masses are released at the top of an inclined plane. The cylinders roll down and the block slides down, all with negligible frictional losses. In what order will they arrive at the bottom?

You have a friend who lives in the southern part of the United States, and you live in the northern part. As Earth rotates, your linear velocity is _ hers, and your angular velocity is __ hers.

A cord attached to a 3.63-kg mass is wrapped around a wheel of radius 0.610 m and released. The moment of inertia of the wheel is 2.71 kg · m². If the wheel rotates on frictionless bearings, the acceleration of the falling weight is

You are pedaling a bicycle at 9.8 m/s. The radius of the wheels of the bicycle is 51.9cm. The angular velocity of rotation of the wheels is

You give an orbiting satellite a command to rotate through an angle given by $\theta$ = at + bt² - ct⁴ Where a, b, and c are constants and $\theta$ is in radians if t is in seconds. What is the angular acceleration of this satellite at time t?

The ball shown in the figure will loop-the-loop if it starts from a point high enough on the incline. When the ball is at point A, the centripetal force on it is best represented by which of the following vectors?

A record turntable rotates through 5.0 rad in 2.8 s as it is accelerated uniformly from rest. What is the angular velocity at the end of that time?

In a laboratory experiment, various torques are applied to a rotor and the angular acceleration is measured. The results are plotted on the accompanying graph. From the graph, the moment of inertia of the rotor is

A solid disk (I = MR²) that is 10 cm in diameter has a mass of 4 kg. The force applied at the outer surface required to produce an angular acceleration of 6 rad/s² about an axis through the center of the disc is

A uniform disk (I_o = ½ mR²) of mass m and radius R is suspended from a point on its rim. The moment of inertia of the disk about an axis perpendicular to the disk through the pivot point 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?

A spherical shell and a solid sphere (both of the same total mass) are rotating about a diameter at the same angular frequency and with the same rotational kinetic energy. What is the ratio of the spherical shell radius to the solid sphere (i.e., R_{spherical shell}/R_{solid sphere}) ?

Exam 9: Rotation

A point P is at a distance R from the axis of rotation of a rigid body. The linear speed, centripetal acceleration, and tangential acceleration of the point can be expressed as

The data used to construct the graph were taken from the tachometer of an airplane. The angular acceleration during the 10 s interval was

A uniform cylinder (I = mR2) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane. The gain in translational kinetic energy of the cylinder when it has rolled 5 m down the incline of the plane is approximately

A solid cylinder, a hollow cylinder, and a square block of equal masses are released at the top of an inclined plane. The cylinders roll down and the block slides down, all with negligible frictional losses. In what order will they arrive at the bottom?

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.

You have a friend who lives in the southern part of the United States, and you live in the northern part. As Earth rotates, your linear velocity is ___________ hers, and your angular velocity is ____________ hers.

A cord attached to a 3.63-kg mass is wrapped around a wheel of radius 0.610 m and released. The moment of inertia of the wheel is 2.71 kg · m2. If the wheel rotates on frictionless bearings, the acceleration of the falling weight is

You are pedaling a bicycle at 9.8 m/s. The radius of the wheels of the bicycle is 51.9cm. The angular velocity of rotation of the wheels is

You give an orbiting satellite a command to rotate through an angle given by θ\thetaθ = at + bt2 - ct4 Where a, b, and c are constants and θ\thetaθ is in radians if t is in seconds. What is the angular acceleration of this satellite at time t?

The ball shown in the figure will loop-the-loop if it starts from a point high enough on the incline. When the ball is at point A, the centripetal force on it is best represented by which of the following vectors?

A record turntable rotates through 5.0 rad in 2.8 s as it is accelerated uniformly from rest. What is the angular velocity at the end of that time?

In a laboratory experiment, various torques are applied to a rotor and the angular acceleration is measured. The results are plotted on the accompanying graph. From the graph, the moment of inertia of the rotor is

A solid disk (I = MR2) that is 10 cm in diameter has a mass of 4 kg. The force applied at the outer surface required to produce an angular acceleration of 6 rad/s2 about an axis through the center of the disc is

A uniform disk (Io = ½ mR2) of mass m and radius R is suspended from a point on its rim. The moment of inertia of the disk about an axis perpendicular to the disk through the pivot point is

A spherical shell and a solid sphere (both of the same total mass) are rotating about a diameter at the same angular frequency and with the same rotational kinetic energy. What is the ratio of the spherical shell radius to the solid sphere (i.e., Rspherical shell/Rsolid sphere) ?

A uniform cylinder (I = mR²) of diameter 0.20 m and mass 12 kg rolls without slipping down a 37º inclined plane. The gain in translational kinetic energy of the cylinder when it has rolled 5 m down the incline of the plane is approximately

You have a friend who lives in the southern part of the United States, and you live in the northern part. As Earth rotates, your linear velocity is _ hers, and your angular velocity is __ hers.

A cord attached to a 3.63-kg mass is wrapped around a wheel of radius 0.610 m and released. The moment of inertia of the wheel is 2.71 kg · m². If the wheel rotates on frictionless bearings, the acceleration of the falling weight is

You give an orbiting satellite a command to rotate through an angle given by $\theta$ = at + bt² - ct⁴ Where a, b, and c are constants and $\theta$ is in radians if t is in seconds. What is the angular acceleration of this satellite at time t?

A solid disk (I = MR²) that is 10 cm in diameter has a mass of 4 kg. The force applied at the outer surface required to produce an angular acceleration of 6 rad/s² about an axis through the center of the disc is

A uniform disk (I_o = ½ mR²) of mass m and radius R is suspended from a point on its rim. The moment of inertia of the disk about an axis perpendicular to the disk through the pivot point is

A spherical shell and a solid sphere (both of the same total mass) are rotating about a diameter at the same angular frequency and with the same rotational kinetic energy. What is the ratio of the spherical shell radius to the solid sphere (i.e., R_{spherical shell}/R_{solid sphere}) ?