Question 1

A 6.0 kg mass in the xy plane is moving in the negative x direction at 3.0 m/s along the line y = 4.0 m. As the mass passes the point (x, y = 10 m, 4.0 m) , what is its angular momentum with respect to the z axis?

Accepted Answer

A)   "30 SI units"
B)   "72 SI units"
C)   "-60 SI units"
D)   "-180 SI units"E) C) and D)
F) B) and D)

Question 2

The Earth's gravity exerts no torque on a satellite orbiting the Earth in an elliptical orbit. Compare the motion of the satellite at the point nearest the Earth (perigee)  to the motion at the point farthest from the Earth (apogee) . At these two points:

Accepted Answer

A)   the tangential velocities are the same.
B)   the angular velocities are the same.
C)   the angular momenta are the same.
D)   the kinetic energies are the same.E) B) and C)
F) A) and D)

Question 3

A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder, with crank, at the top of a well. The moment of inertia of the cylinder and crank is 0.21 kg 2. The bucket is raised to the top of the well and released to fall back into the well. What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 6.0 m/s? A)  2.1 * 103 J B)  1.5 * 103 J C)  0.86 * 103 J D)  0.40 * 103 J" class="answers-bank-image d-inline" rel="preload" > m2. The bucket is raised to the top of the well and released to fall back into the well. What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 6.0 m/s?

Accepted Answer

A)   2.1 * 103 J
B)   1.5 * 103 J
C)   0.86 * 103 J
D)   0.40 * 103 JE) A) and C)
F) All of the above

Question 4

A turntable has a moment of inertia of 3.00 *10-2 kg·m2 and spins freely on a frictionless bearing at 25.0 rev/min. A 0.600-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center. What is the new rate of rotation of the system?

Accepted Answer

A)   20.8 rev/min
B)   22.7 rev/min
C)   33.3 rev/min
D)   27.2 rev/minE) A) and D)
F) All of the above

Question 5

A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 *10-2 -2   , and a radius of 0.10 m. If it rolls down the lane without slipping at a linear speed of 3.0 m/s, what is its total kinetic energy? A)  44 J B)  32 J C)  11 J D)  78 J" class="answers-bank-image d-inline" rel="preload" > , and a radius of 0.10 m. If it rolls down the lane without slipping at a linear speed of 3.0 m/s, what is its total kinetic energy?

Accepted Answer

A)   44 J
B)   32 J
C)   11 J
D)   78 JE) All of the above
F) A) and C)

Question 6

A non-uniform round object of mass M and radius R is found to have its total kinetic energy to be given by  when rolling down an incline. What is this object's moment of inertia?

Accepted Answer

A)   
B)   
C)   
D)   E) A) and D)
F) A) and C)

Question 7

A uniform solid sphere rolls down an incline of height 3 m after starting from rest. In order to calculate its speed at the bottom of the incline, one needs to know:

Accepted Answer

A)   the mass of the sphere.
B)   the radius of the sphere.
C)   the mass and the radius of the sphere.
D)   no more than is given in the problem.E) A) and B)
F) A) and C)

Question 8

The Earth's density increases with depth. If instead the Earth had uniform density, but the same angular velocity and mass, how would its rotational kinetic energy compare to the actual value?

Accepted Answer

A)   It would be the same as the actual value.
B)   It would be less than the actual value.
C)   It would be greater than the actual value.
D)   More information is needed to find the answer.E) A) and B)
F) None of the above

Question 9

An astronaut is on a 100-m lifeline outside a spaceship, circling the ship with an angular speed of 0.100 rad/s. How far inward can she be pulled before the centripetal acceleration reaches 4g = 39.2 m/s2?

Accepted Answer

A)   50.0 m
B)   70.6 m
C)   72.7 m
D)   89.9 mE) None of the above
F) All of the above

Question 10

A Frisbee is thrown horizontally by a student and travels in a straight line. Viewed from above, the Frisbee is seen to be in clockwise rotation. From the point of view of the student, in which direction is the angular momentum of the Frisbee while in flight?

Accepted Answer

A)   The Frisbee has no angular momentum since it is moving along a straight line away from the student.
B)   The direction of the angular momentum is along the line away from the student.
C)   The direction of the angular momentum is toward the right since this was a right-handed throw.
D)   The direction of the angular momentum is downward, perpendicular to the path of the Frisbee.E) A) and B)
F) A) and C)

Question 11

A solid sphere, a solid cylinder, and a hoop each have the same mass and radius. If they are spinning at the same angular velocity, which one has the greatest angular momentum?

Accepted Answer

A)   the sphere
B)   the cylinder
C)   the hoop
D)   They all have the same angular momentum.E) A) and D)
F) All of the above

Question 12

An initially installed flywheel can store 106 J of kinetic energy when rotating at 300 rad/s. It is replaced by another flywheel of the same size but made of a stronger material. If its mass is the same as that of the original, and it is now capable of achieving a rotational speed of 600 rad/s, what maximum energy can be stored?

Accepted Answer

A)   40 *105 J
B)   20 * 105 J
C)   10 * 105 J
D)   5.0 * 105 JE) B) and C)
F) A) and B)

Question 13

A hoop, solid sphere, and solid cylinder each have the same mass and same radius.When rolling down the same incline, which has the greatest torque from gravity on it?

Accepted Answer

A)   the hoop
B)   the sphere
C)   the cylinder
D)   They all have the same torque.E) A) and B)
F) C) and D)

Question 14

A gyroscope has a moment of inertia of 0.140 kg 2 and has an initial angular speed of 12.0 rad/s. If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 *10-2 N   M, then in what time interval will the gyroscope coast from 12.0 rad/s to zero? A)  150 s B)  105 s C)  90.0 s D)  84.0 s" class="answers-bank-image d-inline" rel="preload" > m2 and has an initial angular speed of 12.0 rad/s. If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 *10-2 N 2 and has an initial angular speed of 12.0 rad/s. If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 *10-2 N   M, then in what time interval will the gyroscope coast from 12.0 rad/s to zero? A)  150 s B)  105 s C)  90.0 s D)  84.0 s" class="answers-bank-image d-inline" rel="preload" >
M, then in what time interval will the gyroscope coast from 12.0 rad/s to zero?

Accepted Answer

A)   150 s
B)   105 s
C)   90.0 s
D)   84.0 sE) B) and D)
F) A) and D)

Question 15

A solid disk of radius R rolls down an incline in time T. The center of the disk is removed up to a radius of R/2. The remaining portion of the disk with its center gone is again rolled down the same incline. The time it takes is:

Accepted Answer

A)   T.
B)   more than T.
C)   less than T.
D)   requires more information than given in the problem to figure out.E) C) and D)
F) B) and C)

Question 16

A hoop, a solid sphere, and a solid cylinder each have the same mass, radius, and initial speed and are going up the same inclined plane. Which one goes the farthest?

Accepted Answer

A)   the hoop
B)   the sphere
C)   the cylinder
D)   All go the same distance.E) All of the above
F) A) and C) A

Question 17

A rotating flywheel can be used as a method to store energy. If it has 2.0 * 106 J of kinetic energy when rotating at 400 rad/s, and if a frictional torque of 4.0 N 6 J of kinetic energy when rotating at 400 rad/s, and if a frictional torque of 4.0 N   m acts on the system, in what interval of time would the flywheel come to rest? A)  3.5 min B)  42 min C)  14 min D)  21 min" class="answers-bank-image d-inline" rel="preload" > m acts on the system, in what interval of time would the flywheel come to rest?

Accepted Answer

A)   3.5 min
B)   42 min
C)   14 min
D)   21 minE) B) and D)
F) None of the above

Question 18

An astronomical unit (AU)  is the average distance from the Earth to the Sun. An comet in orbit around the Sun has a perihelion (near point to the Sun)  of 0.50 AU and an aphelion (far point from the Sun)  of 5.0 AU. If the comet's orbital speed at aphelion is v, what is its speed at perihelion?

Accepted Answer

A)   11v
B)   10v
C)   5.5v
D)   4.5vE) None of the above
F) B) and C)

Question 19

A toy gyroscope (a.k.a. a top)  consists of a solid disk with a thin rod projecting perpendicular to the center of the disk. The rod, which serves as the rotational axis for the gyroscope, projects on both sides of the disk. The gyroscope is placed with one end of the axis on the surface of the table, and spun so that the rotation of the disk viewed from above is counterclockwise. Alas, the axis of rotation is not quite perpendicular table surface and so the gyroscope precesses. Viewing from above, with the end of the axis in contact with the table staying in the same spot, in what direction does the other end of the axis of the gyroscope precess?

Accepted Answer

A)   The precession is clockwise.
B)   The precession is counterclockwise.
C)   In the northern hemisphere the precession is clockwise, but in the southern hemisphere it is counterclockwise.
D)   In the northern hemisphere the precession is counterclockwise, but in the southern hemisphere it is clockwise.E) All of the above
F) A) and B) B

Question 20

A figure skater on ice with arms extended, spins at a rate of 3.5 rev/s. After he draws his arms in, he spins at 6.0 rev/s. By what factor does the skater's kinetic energy change when he draws his arms in?

Accepted Answer

A)   2.4
B)   1.7
C)   0.58
D)   0.12E) None of the above
F) All of the above B

Exam 9: Energy and Momentum of Rotational Motion

A 6.0 kg mass in the xy plane is moving in the negative x direction at 3.0 m/s along the line y = 4.0 m. As the mass passes the point (x, y = 10 m, 4.0 m) , what is its angular momentum with respect to the z axis?

Correct Answer
verified

The Earth's gravity exerts no torque on a satellite orbiting the Earth in an elliptical orbit. Compare the motion of the satellite at the point nearest the Earth (perigee) to the motion at the point farthest from the Earth (apogee) . At these two points:

Correct Answer
verified

Correct Answer
verified

A turntable has a moment of inertia of 3.00 *10^-² kg·m² and spins freely on a frictionless bearing at 25.0 rev/min. A 0.600-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center. What is the new rate of rotation of the system?

Correct Answer
verified

A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 *10^-² , and a radius of 0.10 m. If it rolls down the lane without slipping at a linear speed of 3.0 m/s, what is its total kinetic energy?

Correct Answer
verified

A non-uniform round object of mass M and radius R is found to have its total kinetic energy to be given by when rolling down an incline. What is this object's moment of inertia?

Correct Answer
verified

A uniform solid sphere rolls down an incline of height 3 m after starting from rest. In order to calculate its speed at the bottom of the incline, one needs to know:

Correct Answer
verified

The Earth's density increases with depth. If instead the Earth had uniform density, but the same angular velocity and mass, how would its rotational kinetic energy compare to the actual value?

Correct Answer
verified

An astronaut is on a 100-m lifeline outside a spaceship, circling the ship with an angular speed of 0.100 rad/s. How far inward can she be pulled before the centripetal acceleration reaches 4g = 39.2 m/s²?

Correct Answer
verified

A Frisbee is thrown horizontally by a student and travels in a straight line. Viewed from above, the Frisbee is seen to be in clockwise rotation. From the point of view of the student, in which direction is the angular momentum of the Frisbee while in flight?

Correct Answer
verified

A solid sphere, a solid cylinder, and a hoop each have the same mass and radius. If they are spinning at the same angular velocity, which one has the greatest angular momentum?

Correct Answer
verified

Correct Answer
verified

A hoop, solid sphere, and solid cylinder each have the same mass and same radius.When rolling down the same incline, which has the greatest torque from gravity on it?

Correct Answer
verified

A gyroscope has a moment of inertia of 0.140 kg m²and has an initial angular speed of 12.0 rad/s. If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 *10^-² N M, then in what time interval will the gyroscope coast from 12.0 rad/s to zero?

Correct Answer
verified

A solid disk of radius R rolls down an incline in time T. The center of the disk is removed up to a radius of R/2. The remaining portion of the disk with its center gone is again rolled down the same incline. The time it takes is:

Correct Answer
verified

A hoop, a solid sphere, and a solid cylinder each have the same mass, radius, and initial speed and are going up the same inclined plane. Which one goes the farthest?

Correct Answer
verified
A

A rotating flywheel can be used as a method to store energy. If it has 2.0 * 10⁶ J of kinetic energy when rotating at 400 rad/s, and if a frictional torque of 4.0 N m acts on the system, in what interval of time would the flywheel come to rest?

Correct Answer
verified

An astronomical unit (AU) is the average distance from the Earth to the Sun. An comet in orbit around the Sun has a perihelion (near point to the Sun) of 0.50 AU and an aphelion (far point from the Sun) of 5.0 AU. If the comet's orbital speed at aphelion is v, what is its speed at perihelion?

Correct Answer
verified

Correct Answer
verified
B

A figure skater on ice with arms extended, spins at a rate of 3.5 rev/s. After he draws his arms in, he spins at 6.0 rev/s. By what factor does the skater's kinetic energy change when he draws his arms in?

Correct Answer
verified
B

Exam 9: Energy and Momentum of Rotational Motion

A 6.0 kg mass in the xy plane is moving in the negative x direction at 3.0 m/s along the line y = 4.0 m. As the mass passes the point (x, y = 10 m, 4.0 m) , what is its angular momentum with respect to the z axis?

Correct AnswerverifiedShow Answer

The Earth's gravity exerts no torque on a satellite orbiting the Earth in an elliptical orbit. Compare the motion of the satellite at the point nearest the Earth (perigee) to the motion at the point farthest from the Earth (apogee) . At these two points:

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

A turntable has a moment of inertia of 3.00 *10-2 kg·m2 and spins freely on a frictionless bearing at 25.0 rev/min. A 0.600-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center. What is the new rate of rotation of the system?

Correct AnswerverifiedShow Answer

A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 *10-2 , and a radius of 0.10 m. If it rolls down the lane without slipping at a linear speed of 3.0 m/s, what is its total kinetic energy?

Correct AnswerverifiedShow Answer

A non-uniform round object of mass M and radius R is found to have its total kinetic energy to be given by when rolling down an incline. What is this object's moment of inertia?

Correct AnswerverifiedShow Answer

A uniform solid sphere rolls down an incline of height 3 m after starting from rest. In order to calculate its speed at the bottom of the incline, one needs to know:

Correct AnswerverifiedShow Answer

The Earth's density increases with depth. If instead the Earth had uniform density, but the same angular velocity and mass, how would its rotational kinetic energy compare to the actual value?

Correct AnswerverifiedShow Answer

An astronaut is on a 100-m lifeline outside a spaceship, circling the ship with an angular speed of 0.100 rad/s. How far inward can she be pulled before the centripetal acceleration reaches 4g = 39.2 m/s2?

Correct AnswerverifiedShow Answer

A Frisbee is thrown horizontally by a student and travels in a straight line. Viewed from above, the Frisbee is seen to be in clockwise rotation. From the point of view of the student, in which direction is the angular momentum of the Frisbee while in flight?

Correct AnswerverifiedShow Answer

A solid sphere, a solid cylinder, and a hoop each have the same mass and radius. If they are spinning at the same angular velocity, which one has the greatest angular momentum?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

A hoop, solid sphere, and solid cylinder each have the same mass and same radius.When rolling down the same incline, which has the greatest torque from gravity on it?

Correct AnswerverifiedShow Answer

A gyroscope has a moment of inertia of 0.140 kg m2 and has an initial angular speed of 12.0 rad/s. If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 *10-2 N M, then in what time interval will the gyroscope coast from 12.0 rad/s to zero?

Correct AnswerverifiedShow Answer

A solid disk of radius R rolls down an incline in time T. The center of the disk is removed up to a radius of R/2. The remaining portion of the disk with its center gone is again rolled down the same incline. The time it takes is:

Correct AnswerverifiedShow Answer

A hoop, a solid sphere, and a solid cylinder each have the same mass, radius, and initial speed and are going up the same inclined plane. Which one goes the farthest?

Correct AnswerverifiedA

A rotating flywheel can be used as a method to store energy. If it has 2.0 * 106 J of kinetic energy when rotating at 400 rad/s, and if a frictional torque of 4.0 N m acts on the system, in what interval of time would the flywheel come to rest?

Correct AnswerverifiedShow Answer

An astronomical unit (AU) is the average distance from the Earth to the Sun. An comet in orbit around the Sun has a perihelion (near point to the Sun) of 0.50 AU and an aphelion (far point from the Sun) of 5.0 AU. If the comet's orbital speed at aphelion is v, what is its speed at perihelion?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedB

A figure skater on ice with arms extended, spins at a rate of 3.5 rev/s. After he draws his arms in, he spins at 6.0 rev/s. By what factor does the skater's kinetic energy change when he draws his arms in?

Correct AnswerverifiedB

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

A turntable has a moment of inertia of 3.00 *10^-² kg·m² and spins freely on a frictionless bearing at 25.0 rev/min. A 0.600-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center. What is the new rate of rotation of the system?

Correct Answer
verified

A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 *10^-² , and a radius of 0.10 m. If it rolls down the lane without slipping at a linear speed of 3.0 m/s, what is its total kinetic energy?

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

An astronaut is on a 100-m lifeline outside a spaceship, circling the ship with an angular speed of 0.100 rad/s. How far inward can she be pulled before the centripetal acceleration reaches 4g = 39.2 m/s²?

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

A gyroscope has a moment of inertia of 0.140 kg m²and has an initial angular speed of 12.0 rad/s. If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 *10^-² N M, then in what time interval will the gyroscope coast from 12.0 rad/s to zero?

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified
A

A rotating flywheel can be used as a method to store energy. If it has 2.0 * 10⁶ J of kinetic energy when rotating at 400 rad/s, and if a frictional torque of 4.0 N m acts on the system, in what interval of time would the flywheel come to rest?

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified
B

Correct Answer
verified
B