Question 1

The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P ?

A) A
B) B
C) C
D) D 
E) The moment of inertia is the same for all of these objects.

Accepted Answer

B

Question 2

Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied
Perpendicular to the door. Which force has a greater magnitude?
A) the second force (at the doorknob)
B) the first force (at the midpoint)
C) The two forces are equal.

Accepted Answer

Since torque is the product of force and the perpendicular distance from the pivot point (in this case, the door hinge), and both forces produce equal torques, the force applied closer to the hinge (at the midpoint) must be greater in magnitude to compensate for the shorter distance compared to the force applied at the doorknob.

Question 3

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on
A) the mass of the sphere.
B) the radius of the sphere.
C) both the mass and the radius of the sphere.
D) neither the mass nor the radius of the sphere.

Accepted Answer

The linear velocity of a uniform solid sphere rolling without slipping down an inclined plane, starting from rest, depends on the height of the incline and the acceleration due to gravity, but not on the mass or the radius of the sphere. This is because both the translational and rotational kinetic energies at the bottom are determined by the gravitational potential energy lost, which is independent of mass and radius for a given height.

Question 4

As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P  due to this force the greatest?

A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

The answer of As shown in the figure, a given...

Question 5

Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy?
A) Translational kinetic energy is larger.
B) Both are equal.
C) Rotational kinetic energy is larger.
D) You need to know the speed of the hoop to tell.

Accepted Answer

For a hoop rolling without slipping, the translational kinetic energy (associated with the motion of the center of mass) and the rotational kinetic energy (associated with rotation around the center of mass) are equal. This is because the translational kinetic energy is given by (1/2)Mv^2 and the rotational kinetic energy by (1/2)Iω^2, where I is the moment of inertia of the hoop (I = MR^2 for a hoop) and ω is the angular velocity. Since v = ωR for rolling without slipping, both expressions yield the same value for kinetic energy.

Question 6

When a rigid object rotates about a fixed axis, what is true about all the points in the object? (There could be more than one correct choice.)
A) They all have the same radial acceleration.
B) They all have the same tangential speed.
C) They all have the same angular acceleration.
D) They all have the same angular speed.
E) They all have the same tangential acceleration.

Accepted Answer

The answer of When a rigid object rotates about a...

Question 7

A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They are all uniform and roll without slipping. In what order do they reach the bottom?
A) sphere, hoop, disk
B) hoop, disk, sphere
C) sphere, disk, hoop
D) hoop, sphere, disk
E) disk, hoop, sphere

Accepted Answer

The moment of inertia is lowest for the sphere, higher for the disk, and highest for the hoop. Lower moment of inertia means more of the potential energy is converted into translational kinetic energy rather than rotational, allowing the sphere to reach the bottom first, followed by the disk, and then the hoop.

Question 8

Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the
Bottom of the incline first?
A) The large sphere arrives first.
B) The small sphere arrives first.
C) Both reach the bottom at the same time.

Accepted Answer

Both spheres will reach the bottom at the same time because the acceleration of a rolling object down an incline does not depend on its mass or size but only on the gravitational acceleration and the incline angle. Since both spheres are solid and uniform, they have the same distribution of mass relative to their axes of rotation, leading to the same moment of inertia factor in the equation of motion. Therefore, their accelerations are identical, and they reach the bottom simultaneously.

Question 9

Consider a solid uniform sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?
A) Both are equal.
B) Translational kinetic energy is larger.
C) Rotational kinetic energy is larger.
D) You need to know the speed of the sphere to tell.

Accepted Answer

For a solid sphere rolling without slipping, the translational kinetic energy (1/2)Mv^2 is larger than the rotational kinetic energy (1/5)Mv^2.

Question 10

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on
A) the radius of the sphere.
B) the mass of the sphere.
C) both the mass and the radius of the sphere.
D) neither the mass nor the radius of the sphere.

Accepted Answer

The answer of Suppose a solid uniform sphere of mass...

Question 11

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneously at the top of an inclined plane and do not slip, which one will
Reach the bottom first?
A) cylinder
B) sphere
C) pipe
D) The pipe and cylinder arrive together before the sphere.
E) They all reach the bottom at the same time.

Accepted Answer

The solid sphere will reach the bottom first because it has the smallest moment of inertia relative to its mass and radius, allowing it to accelerate faster down the incline compared to the solid cylinder and hollow pipe.

Question 12

A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid
Sphere is
A) less than the total kinetic energy of the cylinder.
B) more than the total kinetic energy of the cylinder.
C) equal to the total kinetic energy of the cylinder.

Accepted Answer

The total kinetic energy of a rolling object is the sum of its translational kinetic energy ($KE_{trans} = \frac{1}{2}mv^2$) and its rotational kinetic energy ($KE_{rot} = \frac{1}{2}I\omega^2$). For both the sphere and the cylinder, the translational kinetic energies are the same because they have the same mass and speed. However, the moment of inertia ($I$) for a solid sphere ($\frac{2}{5}mr^2$) is less than that for a solid cylinder ($\frac{1}{2}mr^2$), making the sphere's rotational kinetic energy less than the cylinder's. Therefore, the total kinetic energy of the sphere is less than that of the cylinder.

Question 13

Two equal-magnitude forces are applied to a door at the doorknob. The first force is applied perpendicular to the door, and the second force is applied at 30° to the plane of the door. Which
Force exerts the greater torque about the door hinge?
A) Both forces exert zero torque.
B) Both forces exert equal non-zero torques.
C) the first force (applied perpendicular to the door)
D) the second force (applied at an angle)

Accepted Answer

The torque exerted by a force depends on the magnitude of the force, the distance from the pivot point (in this case, the door hinge), and the angle at which the force is applied. The first force, being applied perpendicular to the door, exerts a greater torque because the effective lever arm is maximized and the entire force contributes to the torque. The second force, applied at an angle, has a component that acts parallel to the door and does not contribute to the torque, making its effective torque less than that of the first force.

Question 14

A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its Iowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is

A) higher than when it was released.
B) at the same height from which it was released.
C) Iower than when it was released.
D) It is impossible to tell without knowing the mass of the ball.
E) It is impossible to tell without knowing the radius of the ball.

Accepted Answer

The answer of A uniform ball is released from rest...

Question 15

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. If both are uniform, which one reaches the bottom of the incline first if there is no
Slipping?
A) The disk
B) The hoop
C) Both reach the bottom at the same time.

Accepted Answer

The disk reaches the bottom first because it has a smaller moment of inertia compared to the hoop, resulting in a faster acceleration down the incline.

Question 16

Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance from the axis of rotation than Jacques. Which of the following are true statements? (There could be
More than one correct choice.)
A) Jacques and Ahmed have the same tangential speed.
B) Jacques has a smaller angular speed than Ahmed.
C) Ahmed has a greater tangential speed than Jacques.
D) Jacques has a greater angular speed than Ahmed.
E) Jacques and Ahmed have the same angular speed.

Accepted Answer

C) Since Ahmed is at a greater distance from the axis of rotation, he covers more distance in the same amount of time, resulting in a greater tangential speed. E) Angular speed is the same for all points on a rigid rotating body, meaning both Jacques and Ahmed, despite being at different distances from the axis, rotate through the same angles in the same amount of time.

Question 17

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first?
A) the one of greatest mass
B) the sphere
C) the one of smallest diameter
D) the disk
E) They will reach the bottom at the same time.

Accepted Answer

The sphere will reach the bottom first because it has a lower moment of inertia compared to the disk, allowing it to accelerate faster down the incline under the same conditions.

Question 18

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance  r  from the axis of rotation (left), or a distance $r / 2$ from the axis of rotation (right). If you release the hanging blocks simultaneously from rest,

A) both blocks land at the same time.
B) the block at the left lands first.
C) the block at the right lands first.

Accepted Answer

The answer of The rotating systems shown in the figure...

Question 19

A car is traveling along a freeway at 65 mph. What is the linear speed, relative to the
highway, of each of the following points on one of its tires?
(a) the highest point on the tire
(b) the lowest point on a tire
(c) the center of the tire

Accepted Answer

The answer of A car is traveling along a freeway...

Question 20

Five forces act on a rod that is free to pivot at point  P , as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

A) force  A 
B) force B
C) force C
D) force D
E) force E

Accepted Answer

The answer of Five forces act on a rod that...

Quiz 8: Rotational Motion

The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P ?

Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied Perpendicular to the door. Which force has a greater magnitude?

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest?

Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy?

When a rigid object rotates about a fixed axis, what is true about all the points in the object? (There could be more than one correct choice.)

A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They are all uniform and roll without slipping. In what order do they reach the bottom?

Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the Bottom of the incline first?

Consider a solid uniform sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneously at the top of an inclined plane and do not slip, which one will Reach the bottom first?

A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid Sphere is

Two equal-magnitude forces are applied to a door at the doorknob. The first force is applied perpendicular to the door, and the second force is applied at 30° to the plane of the door. Which Force exerts the greater torque about the door hinge?

A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its Iowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. If both are uniform, which one reaches the bottom of the incline first if there is no Slipping?

Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance from the axis of rotation than Jacques. Which of the following are true statements? (There could be More than one correct choice.)

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first?

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left) , or a distance $r / 2$ from the axis of rotation (right) . If you release the hanging blocks simultaneously from rest,

A car is traveling along a freeway at 65 mph. What is the linear speed, relative to the highway, of each of the following points on one of its tires? (a) the highest point on the tire (b) the lowest point on a tire (c) the center of the tire

Five forces act on a rod that is free to pivot at point P , as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

Quiz 8: Rotational Motion

The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P ?

Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied Perpendicular to the door. Which force has a greater magnitude?

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest?

Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy?

When a rigid object rotates about a fixed axis, what is true about all the points in the object? (There could be more than one correct choice.)

A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They are all uniform and roll without slipping. In what order do they reach the bottom?

Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the Bottom of the incline first?

Consider a solid uniform sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneously at the top of an inclined plane and do not slip, which one will Reach the bottom first?

A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid Sphere is

Two equal-magnitude forces are applied to a door at the doorknob. The first force is applied perpendicular to the door, and the second force is applied at 30° to the plane of the door. Which Force exerts the greater torque about the door hinge?

A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its Iowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. If both are uniform, which one reaches the bottom of the incline first if there is no Slipping?

Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance from the axis of rotation than Jacques. Which of the following are true statements? (There could be More than one correct choice.)

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first?

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left) , or a distance r/2r / 2r/2 from the axis of rotation (right) . If you release the hanging blocks simultaneously from rest,

A car is traveling along a freeway at 65 mph. What is the linear speed, relative to the highway, of each of the following points on one of its tires? (a) the highest point on the tire (b) the lowest point on a tire (c) the center of the tire

Five forces act on a rod that is free to pivot at point P , as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left) , or a distance $r / 2$ from the axis of rotation (right) . If you release the hanging blocks simultaneously from rest,