6.7.1 Understanding Conservation of Angular Momentum

Question 1

Understanding Conservation of Angular Momentum

Answer 1

• If the net external torque on a system is equal to zero, then its angular momentum is conserved.
• When an ice skater pulls in her arms to execute a spin, she reduces her moment of inertia. Her increased angular velocity is a result of conservation of angular momentum.
• When some stars grow old, they collapse into neutron stars with very small radii. Because their moment of inertia decreases,their angular velocity increases. Astronomers can detect the radiation from these rotating neutron stars, called pulsars.

Question 2

A figure skater spins in a circle. She begins with her arms outstretched, and her rotation appears to accelerate as she draws her arms toward her body. Which of the following statements describing her motion is not correct?

Answer 2

Because the skater’s rotation accelerates as she brings her arms to her body, her angular momentum must also increase proportionally to the speed of rotation.

Question 3

Given sigma text = dL/dt

which of the following is not correct?

Answer 3

This equation must refer to rotational motion because dL/dt applies only to rotational motion

Question 4

Some large stars turn into neutron stars when they exhaust their nuclear fuel. Consider a star with an initial radius of ri ~ 10^6 km and a rotation rate of one revolution every thirty days. After the star collapses, its final radius is rf ~ km. According to the equation L = Iw, approximately how long will it take for the start to make one revolution after collapse?

Answer 4

0.3 milliseconds

Question 5

Which of the following answers regarding sigma text = 0 is correct?

Answer 5

• The term L is conserved
• delta L = 0
• Li = Lf

Question 6

A skater spinning on ice moves her arms toward her body, increasing her rate of rotation. Which of the following statements regarding her kinetic energy is correct?

Answer 6

• Because her final rotational velocity is larger than her initial rotational velocity, her final kinetic energy must be greater than her initial kinetic energy.
• The increase in the skater’s kinetic energy is due to the energy her body uses to pull her arms in.
• The skater’s kinetic energy increases as she pulls her arms in.

Question 7

A spinning figure skater who varies her rotation by starting with her arms out-stretched and then pulling them toward her body has an initial velocity, wi, an initial moment of inertia, Ii, a final velocity, wf, and a final moment of inertia, If. Which of the following is not correct?

Answer 7

Ifwf > Iiwi

Question 8

Astronomers observe some stellar objects known as pulsars. Which of the following statements regarding these collapsed stars is not correct?

Answer 8

Some of the frequencies produced by pulsars can be detected without amplification on Earth.

Question 9

During a performance, an ice skater begins a spin with her arms outstretched at a rotational velocity of 2.2 revolutions per second. At this instant her moment of inertia is 1.63 kg m^2. As she spins, she pulls in her arms, increasing her rotational velocity. If her moment of inertia is 0.62 kg m^2 after she pulls in her arms, what is her new rotational velocity in revolutions per second?

Answer 9

5.8 revolutions per second

Question 10

Which of the following statements regarding the conservation of angular momentum is not correct?

Answer 10

When some stars grow old, they collapse into neutron stars with very small radii. Because their moment of inertia decreases, their rotational velocity increases. Scientists measure this change in angular momentum by listening to the radio frequencies they emit.