Question 1

A wheel slows down uniformly and comes to rest in 15. seconds. It is rotating initially at 2.0 revolutions per second and has a diameter of 50.cm.
(a) What was the centripetal acceleration at the instant when it was rotating initially?
(b) What was the tangential acceleration?

Accepted Answer

The answer of A wheel slows down uniformly and comes...

Question 2

A wheel of diameter 0.70 m rolls without slipping. A point at the top of the wheel moves with a tangential speed 2.0 m/s.
(a) At what speed is the axis of the wheel moving? 
(b) What is the angular speed of the wheel?

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The answer of A wheel of diameter 0.70 m rolls...

Question 3

A majorette fastens two batons together at their centers to form an X shape. What is the moment of inertia of the combination about an axis through the center of the X if each baton was 1.2 m long and each ball at the end of each baton has a mass of 0.25 kg (assume negligible mass in the rods)?

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The answer of A majorette fastens two batons together at...

Question 4

A triatomic molecule is modeled as follows: mass m is at the origin, mass 2m is at x = a, and mass 3m is at x = 2a.
(a) What is the amount of inertia about the origin? 
(b) What is the moment of inertia about the center of mass?

Accepted Answer

The answer of A triatomic molecule is modeled as follows:...

Question 5

A 2.50 kg is at ( 1.00, 3.00) meters. What is the moment of inertia:
(a) about the x-axis?
(b) about the y-axis?
(c) about the line defined by x= 6.00 m?

Accepted Answer

The answer of A 2.50 kg is at ( 1.00,...

Question 6

A cylinder of radius R and mass M rolls without slipping down a plane inclined at an angle θ above horizontal.
(a) What is the torque about the point of contact with the plane? 
(b) What is the moment of inertia about the point of contact? 
(c) What is the linear speed of the cylinder t seconds after it is released from rest?

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The answer of A cylinder of radius R and mass...

Question 7

Consider a bus designed to obtain its motive power from a large rotating flywheel (1400. kg of diameter 1.5 m) that is periodically brought up to its maximum speed of 3600. rpm by an electric motor at the terminal. If the bus requires an average power of 12. kilowatts, how long will it operate between recharges?

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Question 8

Consider a motorcycle of mass 150. kg, one wheel of which has a mass of 10. kg and a radius of 30. cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

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Question 9

A uniform solid cylinder (mass 100. kg and radius 50.0 cm) is mounted so it is free to rotate about fixed horizontal axis that passes through the centers of its circular ends. A 10.0 kg block is hung from a massless cord wrapped around the cylinder's circumference. When the block is released, the cord unwinds and the block accelerates downward, as shown in Figure 8-2. What is the block's acceleration?

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Question 10

Two children, each of mass 20.0 kg, ride on the perimeter of a small merry-go-round that is rotating at the rate of 1.0 revolution every 4.0 s. The merry-go-round is a disk of mass 30. kg and radius 3.0 m. The children now both move halfway in toward the center to positions 1.5 m from the axis of rotation. Calculate the kinetic energy before and after, and the final rate of rotation. Explain any changes in energy.

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Question 11

A ballerina spins initially at 1.5 revolutions/second when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes 0.88 kg-m² and her angular speed increases to 4.0 rev/s. Determine her initial moment of inertia.

Accepted Answer

The answer of A ballerina spins initially at 1.5 revolutions/second...

Question 12

A solid disk with diameter 2.00 meters and mass 4.0 kg freely rotates about a vertical axis at 36. rpm. A 0.50 kg hunk of bubblegum is dropped onto the disk and sticks to the disk at a distance d = 80. cm from the axis of rotation, as shown in Figure 8-3.
  
(a) What was the moment of inertia before the gum fell?
(b) What was the moment of inertia after the gum stuck?
(c) What is the angular velocity after the gum fell onto the disk?

Accepted Answer

The answer of A solid disk with diameter 2.00 meters...

Question 13

NASA puts a satellite in space which consists of two (32. kg each) masses connected by a 12. meter long light cable, as shown in Figure 8-4. The entire system initially is rotating 4.0 rpm about an axis (at the center of mass) perpendicular to the cable. Motors in each mass reel out more cable so that the masses double their separation (to 24. m).
 
(a) What is the final ROTATIONAL VELOCITY?
(b) The final KINETIC ENERGY is what fraction of the initial?

Accepted Answer

The answer of NASA puts a satellite in space which...

Question 14

A bicycle is moving 4.0 m/s. What is the angular speed of a wheel if its radius is 30.cm?
A) 1.2 rad/s
B) 4.8 rad/s
C) 0.36 rad/s
D) 13. rad/s
E) 7.6 rad/s

Accepted Answer

The answer of A bicycle is moving 4.0 m/s. What...

Question 15

A uniform rod has a weight of 40. N and a length of 1.0 m. It is hinged to a wall (at the left end) , and held in a horizontal position by a vertical massless string (at the right end), as shown in 
 What is the magnitude of the torque exerted by the string about a horizontal axis which passes through the hinge and is perpendicular to the rod?
A) 40 m . N
B) 5.0 m . N
C) 30 m . N
D) 20 m . N
E) 10 m . N

Accepted Answer

The answer of A uniform rod has a weight of...

Question 16

A force is applied to the end of a 2.0 ft long uniform board weighing 50. lb, in order to keep it horizontal, while it pushes against a wall at the left. If the angle the force makes with the board is 30° in the direction shown in Figure 8-6, what is the applied force F?
 
A) 29. lb
B) 58. lb
C) 32. lb
D) 50. lb
E) 90. lb

Accepted Answer

The answer of A force is applied to the end...

Question 17

A boy and a girl are balanced on a massless seesaw. The boy has a mass of 60 kg and the girl's mass is 50 kg. If the boy sits 1.5 m from the pivot point on one side of the seesaw, where must the girl sit on the other side for equilibrium?
A) 3.0 m
B) 1.8 m
C) 1.2 m
D) 1.3 m
E) 2.5 m

Accepted Answer

The answer of A boy and a girl are balanced...

Question 18

Consider two uniform solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is
A) 10.
B) 8.
C) 2.
D) 4.
E) 6.

Accepted Answer

The answer of Consider two uniform solid spheres where one...

Question 19

A 4.0 kg mass is hung from a string which is wrapped around a cylindrical pulley (a cylindrical shell) Figure 8-7 If the mass accelerates downward at 4.90 m/s², what is the mass of the pulley? A) 4.0 kg B) 2.0 kg C) 6.0 kg D) 8.0 kg E) 10.0 kg

Accepted Answer

The answer of A 4.0 kg mass is hung from...

Question 20

A uniform rod has a length of 2.0 m. It is hinged to a wall (at the left end) , and held in a horizontal position by a vertical massless string (at the right end), as shown in Figure 8-8 What is the angular acceleration of the rod at the moment the string is released? A) 15. rad/s² B) It can't be calculated without knowing the rod's mass. C) 3.3 rad/s² D) 7.4 rad/s² E) 11. rad/s²

Accepted Answer

The answer of A uniform rod has a length of...

Quiz 8: Rotational Motion and Equilibrium

A wheel slows down uniformly and comes to rest in 15. seconds. It is rotating initially at 2.0 revolutions per second and has a diameter of 50.cm. (a) What was the centripetal acceleration at the instant when it was rotating initially? (b) What was the tangential acceleration?

A wheel of diameter 0.70 m rolls without slipping. A point at the top of the wheel moves with a tangential speed 2.0 m/s. (a) At what speed is the axis of the wheel moving? (b) What is the angular speed of the wheel?

A majorette fastens two batons together at their centers to form an X shape. What is the moment of inertia of the combination about an axis through the center of the X if each baton was 1.2 m long and each ball at the end of each baton has a mass of 0.25 kg (assume negligible mass in the rods)?

A triatomic molecule is modeled as follows: mass m is at the origin, mass 2m is at x = a, and mass 3m is at x = 2a. (a) What is the amount of inertia about the origin? (b) What is the moment of inertia about the center of mass?

A 2.50 kg is at ( 1.00, 3.00) meters. What is the moment of inertia: (a) about the x-axis? (b) about the y-axis? (c) about the line defined by x= 6.00 m?

Consider a motorcycle of mass 150. kg, one wheel of which has a mass of 10. kg and a radius of 30. cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

A ballerina spins initially at 1.5 revolutions/second when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes 0.88 kg-m² and her angular speed increases to 4.0 rev/s. Determine her initial moment of inertia.

A bicycle is moving 4.0 m/s. What is the angular speed of a wheel if its radius is 30.cm?

A force is applied to the end of a 2.0 ft long uniform board weighing 50. lb, in order to keep it horizontal, while it pushes against a wall at the left. If the angle the force makes with the board is 30° in the direction shown in Figure 8-6, what is the applied force F?

A boy and a girl are balanced on a massless seesaw. The boy has a mass of 60 kg and the girl's mass is 50 kg. If the boy sits 1.5 m from the pivot point on one side of the seesaw, where must the girl sit on the other side for equilibrium?

Consider two uniform solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

A 4.0 kg mass is hung from a string which is wrapped around a cylindrical pulley (a cylindrical shell) Figure 8-7 If the mass accelerates downward at 4.90 m/s², what is the mass of the pulley?

A uniform rod has a length of 2.0 m. It is hinged to a wall (at the left end) , and held in a horizontal position by a vertical massless string (at the right end) , as shown in Figure 8-8 What is the angular acceleration of the rod at the moment the string is released?

Quiz 8: Rotational Motion and Equilibrium

A wheel slows down uniformly and comes to rest in 15. seconds. It is rotating initially at 2.0 revolutions per second and has a diameter of 50.cm. (a) What was the centripetal acceleration at the instant when it was rotating initially? (b) What was the tangential acceleration?

A wheel of diameter 0.70 m rolls without slipping. A point at the top of the wheel moves with a tangential speed 2.0 m/s. (a) At what speed is the axis of the wheel moving? (b) What is the angular speed of the wheel?

A majorette fastens two batons together at their centers to form an X shape. What is the moment of inertia of the combination about an axis through the center of the X if each baton was 1.2 m long and each ball at the end of each baton has a mass of 0.25 kg (assume negligible mass in the rods)?

A triatomic molecule is modeled as follows: mass m is at the origin, mass 2m is at x = a, and mass 3m is at x = 2a. (a) What is the amount of inertia about the origin? (b) What is the moment of inertia about the center of mass?

A 2.50 kg is at ( 1.00, 3.00) meters. What is the moment of inertia: (a) about the x-axis? (b) about the y-axis? (c) about the line defined by x= 6.00 m?

Consider a motorcycle of mass 150. kg, one wheel of which has a mass of 10. kg and a radius of 30. cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

A ballerina spins initially at 1.5 revolutions/second when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes 0.88 kg-m2 and her angular speed increases to 4.0 rev/s. Determine her initial moment of inertia.

A bicycle is moving 4.0 m/s. What is the angular speed of a wheel if its radius is 30.cm?

A force is applied to the end of a 2.0 ft long uniform board weighing 50. lb, in order to keep it horizontal, while it pushes against a wall at the left. If the angle the force makes with the board is 30° in the direction shown in Figure 8-6, what is the applied force F?

A boy and a girl are balanced on a massless seesaw. The boy has a mass of 60 kg and the girl's mass is 50 kg. If the boy sits 1.5 m from the pivot point on one side of the seesaw, where must the girl sit on the other side for equilibrium?

Consider two uniform solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

A 4.0 kg mass is hung from a string which is wrapped around a cylindrical pulley (a cylindrical shell) Figure 8-7 If the mass accelerates downward at 4.90 m/s2, what is the mass of the pulley?

A uniform rod has a length of 2.0 m. It is hinged to a wall (at the left end) , and held in a horizontal position by a vertical massless string (at the right end) , as shown in Figure 8-8 What is the angular acceleration of the rod at the moment the string is released?

A ballerina spins initially at 1.5 revolutions/second when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes 0.88 kg-m² and her angular speed increases to 4.0 rev/s. Determine her initial moment of inertia.

A 4.0 kg mass is hung from a string which is wrapped around a cylindrical pulley (a cylindrical shell) Figure 8-7 If the mass accelerates downward at 4.90 m/s², what is the mass of the pulley?