Question 1

Power can be expressed as the product of

Accepted Answer

A)  force and displacement. 
B)  torque and angular displacement. 
C)  torque and angular acceleration. 
D)  force and acceleration. 
E)  torque and angular velocity. 
A)  force and displacement. 
B)  torque and angular displacement. 
C)  torque and angular acceleration. 
D)  force and acceleration. 
E)  torque and angular velocity. E

Question 2

A wheel of radius R1 has an axle of radius R2 =   R1. If a force F1 is applied tangent to the wheel, a force F2, applied tangent to the axle that will keep the wheel from turning, is equal to

Accepted Answer

A)  F1/4 
B)  F1  
C)  4F1  
D)  16F1  
E)  F1/16 
A)  F1/4 
B)  F1  
C)  4F1  
D)  16F1  
E)  F1/16 C

Question 3

Two masses M and m (M > m) are hung over a disc (Idisc =   M'R2) and are released so that they accelerate. If T1 is the tension in the cord on the left and T2 is the tension in the cord on the right, then

Accepted Answer

A)  T1 = T2  
B)  T2 > T1  
C)  T2 1  
D)  T2 = Mg 
E)  T2 = Mg/m 
A)  T1 = T2  
B)  T2 > T1  
C)  T2 1  
D)  T2 = Mg 
E)  T2 = Mg/m B

Question 4

A ball of mass m1, connected to another mass m2 by a string, is whirled at a constant speed in a horizontal circle of radius R equal to 0.800m. If the mass m2 = 5.00 kg, the kinetic energy of the ball is

Accepted Answer

A)  0.981 J 
B)  2.45 J 
C)  4.90 J 
D)  19.6 J 
E)  39.2 J 
A)  0.981 J 
B)  2.45 J 
C)  4.90 J 
D)  19.6 J 
E)  39.2 J

Question 5

A disc is free to rotate about an axis. A force applied at a distance d from the axis causes an angular acceleration $\alpha$. What angular acceleration is produced if the same force is applied a distance 2d from the axis?

Accepted Answer

A)  $\alpha$ 
B)  2$\alpha$ 
C)  $\alpha$/2 
D)  4$\alpha$ 
E)  $\alpha$/4 
A)  $\alpha$ 
B)  2$\alpha$ 
C)  $\alpha$/2 
D)  4$\alpha$ 
E)  $\alpha$/4

Question 6

Two objects, m1 and m2, both of mass m, are place 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 centripetal acceleration of mass m1 ____ to the centripetal 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 7

Water is drawn from a well in a bucket tied to the end of a rope whose other end wraps around a solid cylinder of mass 50 kg and diameter 25 cm. As this cylinder is turned with a crank, the rope raises the bucket. The mass of a bucket of water is 20 kg. Someone cranks the bucket up and then lets go of the crank, and the bucket of water falls down to the bottom of the well. Without friction or air resistance, what is the angular acceleration of the 50-kg cylinder?

Accepted Answer

A)  1.1 $\times$ 102 rad/s2  
B)  3.6 rad/s2  
C)  35 rad/s2  
D)  63 rad/s2  
E)  17 rad/s2  
A)  1.1 $\times$ 102 rad/s2  
B)  3.6 rad/s2  
C)  35 rad/s2  
D)  63 rad/s2  
E)  17 rad/s2

Question 8

The moment of inertia of a slim rod of mass m and length L about a transverse axis through one end is mL2/3. The moment of inertia of such a rod about a transverse axis through the rod at a distance L/3 from one end is

Accepted Answer

A)  mL2/36 
B)  7mL2/36 
C)  mL2/9 
D)  2mL2/9 
E)  4mL2/9 
A)  mL2/36 
B)  7mL2/36 
C)  mL2/9 
D)  2mL2/9 
E)  4mL2/9

Question 9

A solid cylinder has a moment of inertia of 2 kg · m2. It is at rest at time zero when a net torque given by
$\tau$ = 6t2 + 6 (SI units)
Is applied. After 2 s, the angular velocity of the cylinder will be

Accepted Answer

A)  3.0 rad/s 
B)  12 rad/s 
C)  14 rad/s 
D)  24 rad/s 
E)  28 rad/s 
A)  3.0 rad/s 
B)  12 rad/s 
C)  14 rad/s 
D)  24 rad/s 
E)  28 rad/s

Question 10

The London Eye, which is a giant Ferris wheel, has a diameter of 135 m. It revolves at a constant rate and takes 30 minutes to complete one revolution. What is the linear velocity of a rider in a capsule that is located at the perimeter of the wheel?

Accepted Answer

A)  0.24 m/s 
B)  0.47 m/s 
C)  3.5 m/s 
D)  7.1 m/s 
E)  None of the above 
A)  0.24 m/s 
B)  0.47 m/s 
C)  3.5 m/s 
D)  7.1 m/s 
E)  None of the above

Question 11

The Empire's space station is a long way from any star. It is circular and has a radius of 5.10 km. The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s2 at its circumference is

Accepted Answer

A)  4.4 $\times$ 10-2 rad/s 
B)  7.0 $\times$ 10-3 rad/s 
C)  0.28 rad/s 
D)  - 0.22 rad/s 
E)  1.3 $\times$ 103 rad/s 
A)  4.4 $\times$ 10-2 rad/s 
B)  7.0 $\times$ 10-3 rad/s 
C)  0.28 rad/s 
D)  - 0.22 rad/s 
E)  1.3 $\times$ 103 rad/s

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

A particle moves uniformly around the circumference of a circle whose radius is 8.0 cm with a period of $\pi$/20 s. The angular velocity $\omega$ of the particle is

Accepted Answer

A)  2.5 rad/s 
B)  3.2 $\times$ 102 rad/s 
C)  40 rad/s 
D)  7.9 rad/s 
E)  0.96 rad/s 
A)  2.5 rad/s 
B)  3.2 $\times$ 102 rad/s 
C)  40 rad/s 
D)  7.9 rad/s 
E)  0.96 rad/s

Question 14

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 15

The angular acceleration of the flywheel of a generator is given by
$\alpha$(t) = 6bt - 12ct2
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 16

What constant torque, in the absence of friction, must be applied to a wheel to give it an angular velocity of 50 rad/s if it starts from rest and is accelerated for 10 s? The moment of inertia of the wheel about its axle is 9.0 kg · m2.

Accepted Answer

A)  4.5 N · m 
B)  9.0 N · m 
C)  45 N · m 
D)  30 N · m 
E)  60 N · m 
A)  4.5 N · m 
B)  9.0 N · m 
C)  45 N · m 
D)  30 N · m 
E)  60 N · m

Question 17

The time period for the rotation of the conical pendulum moving in a horizontal circle (bob mass = M, string length L, and vertical half angle $\theta$; see figure) is given by the expression:

Accepted Answer

A)  2 $\pi$ $\times$ {Lcos $\theta$ /g}1/2  
B)  2 $\pi$ $\times$ {Lsin $\theta$/g}1/2  
C)  2 $\pi$ $\times$ Lcos $\theta$ /g 
D)  2 $\pi$ $\times$ Lsin $\theta$ /g 
E)  {2 $\pi$ $\times$ Lcos $\theta$ /g}1/2  
A)  2 $\pi$ $\times$ {Lcos $\theta$ /g}1/2  
B)  2 $\pi$ $\times$ {Lsin $\theta$/g}1/2  
C)  2 $\pi$ $\times$ Lcos $\theta$ /g 
D)  2 $\pi$ $\times$ Lsin $\theta$ /g 
E)  {2 $\pi$ $\times$ Lcos $\theta$ /g}1/2

Question 18

Starting from rest, a disk rotates with constant angular acceleration. If it takes 10 rev to reach an angular velocity $\omega$, then how many additional revolutions are required to reach an angular velocity 2$\omega$?

Accepted Answer

A)  10 rev 
B)  20 rev 
C)  30 rev 
D)  40 rev 
E)  50 rev 
A)  10 rev 
B)  20 rev 
C)  30 rev 
D)  40 rev 
E)  50 rev

Question 19

A 5 $\times$ 10-6-kg dot of paint on the side of a rotating cylinder flies off when the angular speed of the cylinder reaches 5 $\times$ 103 rad/s. The spin axis of the cylinder is vertical and its radius is 0.04 m. The force of adhesion between the paint and the surface is approximately

Accepted Answer

A)  1 N 
B)  1 mN 
C)  5 mN 
D)  5 kN 
E)  5 N 
A)  1 N 
B)  1 mN 
C)  5 mN 
D)  5 kN 
E)  5 N

Question 20

The disc brakes of a high performance car are often made of carbon fiber instead of iron, thereby reducing the mass. If both types of discs are of the same size and shape, and each iron disc has a mass of 4 kg and each carbon disc has a mass of 1 kg, what is the reduction in rotational kinetic energy at 72 km/h if all the four iron discs in the car are replaced with carbon discs?

Accepted Answer

A)  300 J 
B)  400 J 
C)  800 J 
D)  1200 J 
E)  1600 J 
A)  300 J 
B)  400 J 
C)  800 J 
D)  1200 J 
E)  1600 J

Power can be expressed as the product of

A wheel of radius R₁ has an axle of radius R₂ = R₁. If a force F₁ is applied tangent to the wheel, a force F₂, applied tangent to the axle that will keep the wheel from turning, is equal to

Two masses M and m (M > m) are hung over a disc (I_dis_c = M'R²) and are released so that they accelerate. If T₁ is the tension in the cord on the left and T₂ is the tension in the cord on the right, then

A ball of mass m₁, connected to another mass m₂ by a string, is whirled at a constant speed in a horizontal circle of radius R equal to 0.800m. If the mass m₂ = 5.00 kg, the kinetic energy of the ball is

A disc is free to rotate about an axis. A force applied at a distance d from the axis causes an angular acceleration $\alpha$ . What angular acceleration is produced if the same force is applied a distance 2d from the axis?

The moment of inertia of a slim rod of mass m and length L about a transverse axis through one end is mL²/3. The moment of inertia of such a rod about a transverse axis through the rod at a distance L/3 from one end is

A solid cylinder has a moment of inertia of 2 kg · m². It is at rest at time zero when a net torque given by $\tau$ = 6t² + 6 (SI units) Is applied. After 2 s, the angular velocity of the cylinder will be

The London Eye, which is a giant Ferris wheel, has a diameter of 135 m. It revolves at a constant rate and takes 30 minutes to complete one revolution. What is the linear velocity of a rider in a capsule that is located at the perimeter of the wheel?

The Empire's space station is a long way from any star. It is circular and has a radius of 5.10 km. The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s² at its circumference is

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

A particle moves uniformly around the circumference of a circle whose radius is 8.0 cm with a period of $\pi$ /20 s. The angular velocity $\omega$ of the particle is

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

The angular acceleration of the flywheel of a generator is given by $\alpha$ (t) = 6bt - 12ct² 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

What constant torque, in the absence of friction, must be applied to a wheel to give it an angular velocity of 50 rad/s if it starts from rest and is accelerated for 10 s? The moment of inertia of the wheel about its axle is 9.0 kg · m².

Starting from rest, a disk rotates with constant angular acceleration. If it takes 10 rev to reach an angular velocity $\omega$ , then how many additional revolutions are required to reach an angular velocity 2 $\omega$ ?

A 5 $\times$ 10^-6-kg dot of paint on the side of a rotating cylinder flies off when the angular speed of the cylinder reaches 5 $\times$ 10³ rad/s. The spin axis of the cylinder is vertical and its radius is 0.04 m. The force of adhesion between the paint and the surface is approximately

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

Filters

Exam 9: Rotation

Power can be expressed as the product of

A wheel of radius R1 has an axle of radius R2 = R1. If a force F1 is applied tangent to the wheel, a force F2, applied tangent to the axle that will keep the wheel from turning, is equal to

Two masses M and m (M > m) are hung over a disc (Idisc = M'R2) and are released so that they accelerate. If T1 is the tension in the cord on the left and T2 is the tension in the cord on the right, then

A ball of mass m1, connected to another mass m2 by a string, is whirled at a constant speed in a horizontal circle of radius R equal to 0.800m. If the mass m2 = 5.00 kg, the kinetic energy of the ball is

A disc is free to rotate about an axis. A force applied at a distance d from the axis causes an angular acceleration α\alphaα . What angular acceleration is produced if the same force is applied a distance 2d from the axis?

Two objects, m1 and m2, both of mass m, are place 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 centripetal acceleration of mass m1 ____ to the centripetal acceleration of m2.

The moment of inertia of a slim rod of mass m and length L about a transverse axis through one end is mL2/3. The moment of inertia of such a rod about a transverse axis through the rod at a distance L/3 from one end is

A solid cylinder has a moment of inertia of 2 kg · m2. It is at rest at time zero when a net torque given by τ\tauτ = 6t2 + 6 (SI units) Is applied. After 2 s, the angular velocity of the cylinder will be

The London Eye, which is a giant Ferris wheel, has a diameter of 135 m. It revolves at a constant rate and takes 30 minutes to complete one revolution. What is the linear velocity of a rider in a capsule that is located at the perimeter of the wheel?

The Empire's space station is a long way from any star. It is circular and has a radius of 5.10 km. The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s2 at its circumference is

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

A particle moves uniformly around the circumference of a circle whose radius is 8.0 cm with a period of π\piπ /20 s. The angular velocity ω\omegaω of the particle is

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

The angular acceleration of the flywheel of a generator is given by α\alphaα (t) = 6bt - 12ct2 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

What constant torque, in the absence of friction, must be applied to a wheel to give it an angular velocity of 50 rad/s if it starts from rest and is accelerated for 10 s? The moment of inertia of the wheel about its axle is 9.0 kg · m2.

The time period for the rotation of the conical pendulum moving in a horizontal circle (bob mass = M, string length L, and vertical half angle θ\thetaθ ; see figure) is given by the expression:

Starting from rest, a disk rotates with constant angular acceleration. If it takes 10 rev to reach an angular velocity ω\omegaω , then how many additional revolutions are required to reach an angular velocity 2 ω\omegaω ?

A 5 ×\times× 10-6-kg dot of paint on the side of a rotating cylinder flies off when the angular speed of the cylinder reaches 5 ×\times× 103 rad/s. The spin axis of the cylinder is vertical and its radius is 0.04 m. The force of adhesion between the paint and the surface is approximately

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

Filters

A wheel of radius R₁ has an axle of radius R₂ = R₁. If a force F₁ is applied tangent to the wheel, a force F₂, applied tangent to the axle that will keep the wheel from turning, is equal to

Two masses M and m (M > m) are hung over a disc (I_dis_c = M'R²) and are released so that they accelerate. If T₁ is the tension in the cord on the left and T₂ is the tension in the cord on the right, then

A ball of mass m₁, connected to another mass m₂ by a string, is whirled at a constant speed in a horizontal circle of radius R equal to 0.800m. If the mass m₂ = 5.00 kg, the kinetic energy of the ball is

A disc is free to rotate about an axis. A force applied at a distance d from the axis causes an angular acceleration $\alpha$ . What angular acceleration is produced if the same force is applied a distance 2d from the axis?

The moment of inertia of a slim rod of mass m and length L about a transverse axis through one end is mL²/3. The moment of inertia of such a rod about a transverse axis through the rod at a distance L/3 from one end is

A solid cylinder has a moment of inertia of 2 kg · m². It is at rest at time zero when a net torque given by $\tau$ = 6t² + 6 (SI units) Is applied. After 2 s, the angular velocity of the cylinder will be

The Empire's space station is a long way from any star. It is circular and has a radius of 5.10 km. The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s² at its circumference is

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

A particle moves uniformly around the circumference of a circle whose radius is 8.0 cm with a period of $\pi$ /20 s. The angular velocity $\omega$ of the particle is

The angular acceleration of the flywheel of a generator is given by $\alpha$ (t) = 6bt - 12ct² 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

What constant torque, in the absence of friction, must be applied to a wheel to give it an angular velocity of 50 rad/s if it starts from rest and is accelerated for 10 s? The moment of inertia of the wheel about its axle is 9.0 kg · m².

Starting from rest, a disk rotates with constant angular acceleration. If it takes 10 rev to reach an angular velocity $\omega$ , then how many additional revolutions are required to reach an angular velocity 2 $\omega$ ?

A 5 $\times$ 10^-6-kg dot of paint on the side of a rotating cylinder flies off when the angular speed of the cylinder reaches 5 $\times$ 10³ rad/s. The spin axis of the cylinder is vertical and its radius is 0.04 m. The force of adhesion between the paint and the surface is approximately