Question 1

Conservation of angular momentum: A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure). The ball is covered with glue, so it sticks to the bar. During this collision

Accepted Answer

The angular momentum of the system (ball and bar) is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook. The only external force acting on the system is the collision between the ball and the bar, but this force does not produce any torque about the hook. Therefore, the angular momentum of the system is conserved.

Question 2

Basic rotational quantities: When you ride a bicycle, in what direction is the angular velocity of the wheels?

Accepted Answer

A

Question 3

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

Accepted Answer

B

Question 4

Rotational kinematics: The angular velocity of a 755-g wheel 15.0 cm in diameter is given by the equation ω(t) = (2.00 rad/s²)t + (1.00 rad/s⁴)t³. (a) Through how many radians does the wheel turn during the first 2.00 s of its motion? (b) What is the angular acceleration (in rad/s²) of the wheel at the end of the first 2.00 s of its motion?

Accepted Answer

The answer of Rotational kinematics: The angular velocity of a...

Question 5

Rotational kinematics: A turbine blade rotates with angular velocity ω(t) = 2.00 rad/s- 2.1.00 rad/s³ . What is the angular acceleration of the blade at

Accepted Answer

The answer of Rotational kinematics: A turbine blade rotates with...

Question 6

Rotational kinematics: The angular acceleration of a wheel is given in  by  where t is in seconds. If the wheel starts from rest at  when is the next time the wheel is at rest?

Accepted Answer

The answer of Rotational kinematics: The angular acceleration of a...

Question 7

Basic rotational quantities: When a rigid body rotates about a fixed axis, all the points in the body have the same

Accepted Answer

When a rigid body rotates about a fixed axis, all points in the body experience the same angular acceleration because they are all bound to the same rotational motion and rate of change of angular velocity.

Question 8

Rotational dynamics about a fixed axis: The two rotating systems shown in the figure differ only in that the two identical movable masses are positioned at different distances from the axis of rotation. If you release the hanging blocks simultaneously from rest, and if the ropes do not slip, which block lands first?

Accepted Answer

The block on the right lands first. This is because it is closer to the axis of rotation, meaning it has a smaller radius and therefore a smaller moment of inertia. According to the law of conservation of energy, the total energy of the system is conserved. Therefore, the potential energy of the blocks is converted to kinetic energy as they fall. The block with the smaller moment of inertia can accelerate faster and therefore reaches the ground first.

Question 9

Rolling: A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire), its velocity with respect to the road is

Accepted Answer

When a tire rolls without slipping, the velocity of any point on the tire relative to the center of the tire is equal to the velocity of the tire itself (v). When the tape is at the top of the tire, its velocity relative to the road is the sum of the tire's translational velocity (v) and the velocity of the tape relative to the center of the tire (also v), resulting in a total velocity of 2v.

Question 10

Rotational dynamics about a moving axis: If an irregularly shaped object (such as a wrench) is dropped from rest in a classroom and feels no air resistance, it will

Accepted Answer

The answer of Rotational dynamics about a moving axis: If...

Question 11

Equilibrium: If the torque on an object adds up to zero

Accepted Answer

An object can have zero net torque and still be in rotational motion if it was already rotating. Zero net torque means no change in rotational motion, but it doesn't imply zero net force or linear acceleration.

Question 12

Conservation of angular momentum: The angular momentum of a system remains constant

Accepted Answer

Conservation of angular momentum is only valid when no net external torque acts on the system. It is independent of the linear momentum and energy of the system, so choices A and C are incorrect. While it is a conserved quantity, choice E is too general and not specific to the conditions required for conservation.

Question 13

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

Accepted Answer

For a rolling sphere, translational kinetic energy is (1/2)Mv^2 and rotational kinetic energy is (1/2)Iω^2. For a solid sphere, I = (2/5)MR^2 and ω = v/R, so rotational kinetic energy becomes (1/5)Mv^2. Thus, translational kinetic energy is larger.

Question 14

Rolling: A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii and are of uniform density. If the three are released simultaneously at the top of an inclined plane and roll without slipping, which one will reach the bottom first?

Accepted Answer

The solid sphere reaches the bottom first because it has the smallest moment of inertia, which means it accelerates faster when rolling without slipping.

Question 15

Moment of inertia: A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I₁ is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I₂ is the moment of inertia with respect to an axis passing through one of the masses, it follows that

Accepted Answer

The moment of inertia depends on the distribution of mass relative to the axis of rotation. For $I_{\text{₁}}$, both masses are equidistant from the axis, leading to a certain moment of inertia. For $I_{\text{₂}}$, one mass is at the axis (contributing zero to the moment of inertia) and the other is twice as far compared to the first case, leading to a greater moment of inertia due to the square of the distance factor in the moment of inertia formula ($I = mr^2$).

Question 16

Equilibrium: A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw? Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses.

Accepted Answer

Since both people are moving the same distance from the pivot point, their weight distribution on the seesaw remains unchanged. This means that the seesaw will still be balanced in the same position.

Question 17

Basic rotational quantities: A horizontal disk rotates about a vertical axis through its center. Point P is midway between the center and the rim of the disk, and point Q is on the rim. If the disk turns with constant angular velocity, which of the following statements about it are true? (There may be more than one correct choice.)

Accepted Answer

The answer of Basic rotational quantities: A horizontal disk rotates...

Question 18

Rotational kinematics with constant angular acceleration: A 1.15-kg grinding wheel 22.0 cm in diameter is spinning counterclockwise at a rate of 20.0 revolutions per second. When the power to the grinder is turned off, the grinding wheel slows with constant angular acceleration and takes 80.0 s to come to a rest. (a) What was the angular acceleration (in rad/s²) of the grinding wheel as it came to rest if we take a counterclockwise rotation as positive? (b) How many revolutions did the wheel make during the time it was coming to rest?

Accepted Answer

The answer of Rotational kinematics with constant angular acceleration: A...

Question 19

Basic rotational quantities: As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?

Accepted Answer

The answer of Basic rotational quantities: As you are leaving...

Question 20

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

Accepted Answer

The solid sphere will reach the bottom first because it has the highest rotational inertia and will therefore experience the lowest acceleration down the ramp. The disk will reach the bottom second because it has a lower rotational inertia than the hoop. The hoop will reach the bottom last because it has the lowest rotational inertia and will experience the highest acceleration down the ramp, but it will take longer to reach the bottom due to its larger circumference. Therefore the correct order is sphere, disk, hoop.

Quiz 8: Momentum, Impulse, and Collisions

Conservation of angular momentum: A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure) . The ball is covered with glue, so it sticks to the bar. During this collision

Basic rotational quantities: When you ride a bicycle, in what direction is the angular velocity of the wheels?

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

Rotational kinematics: A turbine blade rotates with angular velocity ω(t) = 2.00 rad/s- 2.1.00 rad/s³ . What is the angular acceleration of the blade at

Rotational kinematics: The angular acceleration of a wheel is given in by where t is in seconds. If the wheel starts from rest at when is the next time the wheel is at rest?

Basic rotational quantities: When a rigid body rotates about a fixed axis, all the points in the body have the same

Rolling: A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire) , its velocity with respect to the road is

Rotational dynamics about a moving axis: If an irregularly shaped object (such as a wrench) is dropped from rest in a classroom and feels no air resistance, it will

Equilibrium: If the torque on an object adds up to zero

Conservation of angular momentum: The angular momentum of a system remains constant

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

Rolling: A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii and are of uniform density. If the three are released simultaneously at the top of an inclined plane and roll without slipping, which one will reach the bottom first?

Basic rotational quantities: As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?

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

Quiz 8: Momentum, Impulse, and Collisions

Conservation of angular momentum: A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure) . The ball is covered with glue, so it sticks to the bar. During this collision

Basic rotational quantities: When you ride a bicycle, in what direction is the angular velocity of the wheels?

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

Rotational kinematics: A turbine blade rotates with angular velocity ω(t) = 2.00 rad/s- 2.1.00 rad/s3 . What is the angular acceleration of the blade at

Rotational kinematics: The angular acceleration of a wheel is given in by where t is in seconds. If the wheel starts from rest at when is the next time the wheel is at rest?

Basic rotational quantities: When a rigid body rotates about a fixed axis, all the points in the body have the same

Rolling: A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire) , its velocity with respect to the road is

Rotational dynamics about a moving axis: If an irregularly shaped object (such as a wrench) is dropped from rest in a classroom and feels no air resistance, it will

Equilibrium: If the torque on an object adds up to zero

Conservation of angular momentum: The angular momentum of a system remains constant

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

Rolling: A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii and are of uniform density. If the three are released simultaneously at the top of an inclined plane and roll without slipping, which one will reach the bottom first?

Basic rotational quantities: As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?

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

Rotational kinematics: A turbine blade rotates with angular velocity ω(t) = 2.00 rad/s- 2.1.00 rad/s³ . What is the angular acceleration of the blade at