Q: A net external torque acts on a rotating object for a short time interval $$\Delta t. $$Which equation describes the resulting change in angular momentum?

$$\tau_{net}\Delta t = \Delta L$$

Question 1

A rocket is initially at rest in space. When its fuel is ignited, exhaust gases are expelled backward. According to the law of conservation of momentum, what happens to the rocket as the gases are expelled?

Accepted Answer

The rocket moves forward so that the total momentum remains zero.

Question 2

Two ice skaters, initially at rest, push off from one another. Skater A has a mass of 50 kg and skater B has a mass of 75 kg. If skater A moves away at 3 m/s, what is the velocity of skater B?

Accepted Answer

$$v_B = -2\ \mathrm{m/s}$$

Question 3

A 1 kg box moving at $$4\ \mathrm{m/s} to $$the left and a 2 kg box at rest on a frictionless surface explode apart. If the 1 kg box moves at $$4\ \mathrm{m/s} to $$the left after the explosion, what is the velocity of the 2 kg box?

Accepted Answer

$$2\ \mathrm{m/s}$$\ to\ the\ right$

Question 4

Which of the following best describes a perfectly inelastic collision?

Accepted Answer

The objects stick together and move with a common velocity after the collision.

Question 5

A 0.80 kg falcon dives at $$18\ \mathrm{m/s} at a$$ $$45^\circ$$ angle and grabs a 0.36 kg pigeon flying horizontally at $$9.0\ \mathrm{m/s}. $$What is the magnitude of their combined velocity immediately after the collision?

Accepted Answer

$$15\ \mathrm{m/s}$$

Question 6

In a two-dimensional collision, which of the following must be conserved?

Accepted Answer

Both the x- and y-components of momentum

Question 7

A billiard ball strikes a group of stationary balls and they scatter in various directions. Which principle allows you to predict the motion of the balls after the collision?

Accepted Answer

Conservation of total momentum

Question 8

A figure skater pulls in her arms during a spin, reducing her moment of inertia to half its original value. If her initial angular velocity was $$\omega_i$$, what is her final angular velocity $$\omega_f$$?

Accepted Answer

$$\omega_f = 2\omega_i$$

Question 9

Which equation correctly expresses the law of conservation of angular momentum for a system of two objects?

Accepted Answer

$$I_{1f}\omega_{1f} + I_{2f}\omega_{2f} = I_{1i}\omega_{1i} + I_{2i}\omega_{2i}$$

Question 10

A 36 kg child stands at the center of a 200 kg merry-go-round (radius 2.0 m) rotating every 2.5 s. If the child walks to the edge, what happens to the period of rotation?

Accepted Answer

It increases because the moment of inertia increases.

Question 11

Which of the following is the correct formula for the angular momentum $$L of a $$rotating object?

Accepted Answer

$$L = I\omega$$

Question 12

A net external torque acts on a rotating object for a short time interval $$\Delta t. $$Which equation describes the resulting change in angular momentum?

Accepted Answer

$$	au_{net}\Delta t = \Delta L$$

Question 13

A clay ball of mass $$m_1$$ moving at velocity $$v_1$$ collides and sticks to a stationary block of mass $$m_2. $$What is their common velocity after the collision?

Accepted Answer

$$v_f = \frac{m_1$ v_1$}{m_1$ + m_2$}$$

Question 14

Which of the following statements about explosions is correct?

Accepted Answer

Explosions involve internal forces and conserve total momentum if the system is isolated.

Question 15

A system is isolated and undergoes a collision in two dimensions. Which of the following must be true?

Accepted Answer

The total vector sum of momentum before and after the collision is the same.

Question 16

A rotating disk has a moment of inertia $$I$$ and angular velocity $$\omega. If no $$external torque acts on it and its moment of inertia increases to $$2I$$, what happens to its angular velocity?

Accepted Answer

$$\omega$$ decreases to $$\omega/2$$

Question 17

Which of the following is NOT a necessary step in solving a conservation of momentum problem?

Accepted Answer

Assuming kinetic energy is always conserved

Chapter 9: Momentum and Angular Momentum – Study Notes

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