Chapter 9: Rotational Motion and Angular Momentum - Review Questions

What is the unit of angular acceleration?

a) m/s²

b) rad/s²

c) rpm

d) m/s

b) rad/s²

In which direction is angular acceleration considered positive according to the sign convention?

a) Clockwise

b) Counterclockwise

c) Upward

d) Downward

b) Counterclockwise

What happens to angular acceleration when a skater pulls in her arms while spinning?

a) It remains constant

b) It increases

c) It decreases

d) It becomes zero

b) It increases

What is the relationship between tangential acceleration and angular acceleration?

a) at = αr

b) at = α/r

c) at = r/α

d) at = α²r

a) at = αr

Angular acceleration is defined as the rate of change of angular ___.

velocity

In circular motion, linear acceleration is called ___ acceleration.

tangential

Explain how angular acceleration is related to linear acceleration in circular motion.

Angular acceleration is related to linear acceleration through the equation at = αr, where at is the tangential acceleration, α is the angular acceleration, and r is the radius of the circular path.

What is the significance of the sign of angular acceleration?

The sign of angular acceleration indicates the direction of the acceleration. A positive sign denotes counterclockwise acceleration, while a negative sign denotes clockwise acceleration.

What is the angular acceleration if a wheel's angular velocity changes from 0 to 220 rad/s in 2 seconds?

a) 110 rad/s^2

b) 220 rad/s^2

c) 55 rad/s^2

d) 440 rad/s^2

a) 110 rad/s^2

In rotational kinematics, what is the equivalent of linear displacement?

a) Angular displacement (θ)

b) Angular velocity (ω)

c) Angular acceleration (α)

d) Time (t)

a) Angular displacement (θ)

The equation relating angular velocity, initial angular velocity, angular acceleration, and time is ___.

ω = ω0 + αt

In rotational motion, angular displacement is analogous to ___ in translational motion.

linear displacement

What is the rotational analog of force in Newton's second law?

a) Torque

b) Moment of inertia

c) Angular velocity

d) Linear acceleration

a) Torque

Which of the following factors does NOT affect torque?

a) Force magnitude

b) Force direction

c) Point of application

d) Mass of the object

d) Mass of the object

How does the moment of inertia affect angular acceleration for a given torque?

a) Larger moment of inertia results in larger angular acceleration

b) Larger moment of inertia results in smaller angular acceleration

c) Moment of inertia does not affect angular acceleration

d) Moment of inertia only affects linear acceleration

b) Larger moment of inertia results in smaller angular acceleration

The moment of inertia of a hoop with mass M and radius R is given by ___.

MR^2

The equation τ = Iα is the rotational analog of Newton's second law, where τ represents ___, I represents ___, and α represents ___.

torque; moment of inertia; angular acceleration

Explain how the distribution of mass affects the moment of inertia of an object.

The moment of inertia depends not only on the mass of an object but also on how that mass is distributed relative to the axis of rotation. Mass further from the axis increases the moment of inertia more than mass closer to the axis.

What is the relationship between torque and angular acceleration in rotational dynamics?

In rotational dynamics, torque is directly proportional to angular acceleration, with the moment of inertia being the proportionality constant. This relationship is expressed as τ = Iα.

What is the expression for rotational work?

a) net W = net τθ

b) net W = net F Δs

c) net W = Iαθ

d) net W = 1/2 Iω²

a) net W = net τθ

Which of the following is analogous to mass in the expression for rotational kinetic energy?

a) Torque

b) Moment of Inertia

c) Angular Velocity

d) Force

b) Moment of Inertia

What is the work-energy theorem for rotational motion?

a) net W = 1/2 Iω² - 1/2 Iω₀²

b) net W = net τθ

c) net W = Iαθ

d) net W = 1/2 mv²

a) net W = 1/2 Iω² - 1/2 Iω₀²

How is angular velocity related to rotational kinetic energy?

a) It is directly proportional to rotational kinetic energy.

b) It is inversely proportional to rotational kinetic energy.

c) Rotational kinetic energy is proportional to the square of angular velocity.

d) Rotational kinetic energy is independent of angular velocity.

c) Rotational kinetic energy is proportional to the square of angular velocity.

What happens to the rotational kinetic energy when a helicopter's blades slow down below a critical angular velocity?

a) It increases.

b) It decreases.

c) It remains constant.

d) It becomes zero.

b) It decreases.

The expression for rotational kinetic energy is given by KE_rot = ___ Iω².

1/2

In rotational motion, torque is analogous to ___ in translational motion.

force

The moment of inertia for a disk is given by I = ___ MR².

1/2

Explain how rotational work is analogous to translational work.

Rotational work is analogous to translational work in that both involve the product of a force-like quantity and a displacement-like quantity. In rotational work, torque is analogous to force, and angular displacement is analogous to linear displacement.

Describe the relationship between torque, moment of inertia, and angular acceleration.

Torque is equal to the product of moment of inertia and angular acceleration, expressed as τ = Iα. This relationship is analogous to Newton's second law for rotation.

How does the conservation of mechanical energy apply to rotational motion?

In rotational motion, the conservation of mechanical energy states that the sum of rotational kinetic energy and potential energy remains constant in a closed system, similar to translational motion.

Which of the following is conserved when the net external torque is zero?

a) Angular Momentum

b) Linear Momentum

c) Kinetic Energy

d) Potential Energy

a) Angular Momentum

What happens to the angular velocity of a figure skater when she pulls her arms in?

a) It increases

b) It decreases

c) It remains the same

d) It becomes zero

a) It increases

What is the relationship between torque and angular momentum?

a) net τ = ΔL/Δt

b) net τ = Fd

c) net τ = mv

d) net τ = 1/2 mv^2

a) net τ = ΔL/Δt

The law of conservation of angular momentum states that if the net external torque is zero, then angular momentum is ___.

conserved

Explain why an ice skater spins faster when she pulls her arms in.

When an ice skater pulls her arms in, her moment of inertia decreases. To conserve angular momentum, her angular velocity must increase, causing her to spin faster.

What is the significance of the relationship net τ = ΔL/Δt in rotational motion?

The relationship net τ = ΔL/Δt signifies that the net torque acting on a system is equal to the rate of change of its angular momentum, analogous to Newton's second law for linear motion.

What is the percussion point in the context of collisions?

a) The point where maximum force is exerted

b) The point where no force is exerted on the pivot

c) The point where the object breaks

d) The point of maximum vibration

b) The point where no force is exerted on the pivot

In a collision where a disk strikes a stick nailed at one end, the angular momentum is conserved because the external force exerts no ___.

torque

The percussion point is the point on an object where striking it results in no force on the ___.

pivot

What does the right-hand rule help determine in the context of angular momentum?

a) The magnitude of angular momentum

b) The direction of angular momentum

c) The speed of rotation

d) The mass of the rotating object

b) The direction of angular momentum

What happens to a gyroscope when it is spinning and a torque is applied?

a) It stops spinning

b) It precesses around a vertical axis

c) It falls over

d) It spins faster

b) It precesses around a vertical axis

How does torque affect angular momentum?

a) It changes only the magnitude

b) It changes only the direction

c) It changes both magnitude and direction

d) It has no effect

c) It changes both magnitude and direction

Why does Earth precess like a gyroscope?

a) Due to its spherical shape

b) Due to the torque from the Sun and Moon

c) Because it is not spinning

d) Because of its magnetic field

b) Due to the torque from the Sun and Moon

The right-hand rule is used to determine the ___ of angular momentum.

direction

A gyroscope precesses around a ___ axis when a torque is applied.

vertical