Question 1

Which of the following statements about elastic collisions is correct?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 2

A curling stone of mass $$M$$ moving at $$2\ \mathrm{m/s}$$ collides elastically with an identical stone at rest. After the collision, the first stone moves at $$1\ \mathrm{m/s}. $$What is the speed of the second stone?

Accepted Answer

$$\sqrt{3}\ \mathrm{m/s}$$

Question 3

In a 2D elastic collision between two equal masses, what is the angle between their final velocities?

Accepted Answer

$$90^\circ$$

Question 4

Which equation correctly relates momentum and kinetic energy for non-relativistic speeds?

Accepted Answer

$$KE = \frac{p^2$}{2m}$$

Question 5

For a hydrogen atom, the center of mass is closest to which particle?

Accepted Answer

The proton

Question 6

Given masses $$m_1$$ and $$m_2 at $$positions $$x_1$$ and $$x_2$$, what is the formula for the center of mass in 1D?

Accepted Answer

$$x_{cm} = \frac{m_1x_1 + m_2x_2}{m_1$ + m_2$}$$

Question 7

A rocket expels propellant at a constant rate. Which equation gives the change in velocity ($$\Delta v) of $$the rocket?

Accepted Answer

$$\Delta v = u \ln\left(\frac{m_0$}{m_f}\right)$$

Question 8

Which of the following best describes the reduced mass $$\mu$$ for two-body systems?

Accepted Answer

$$\mu = \frac{m_1$ m_2$}{m_1$ + m_2$}$$

Question 9

In particle physics, why do we often use the center of mass reference frame for collisions?

Accepted Answer

Because the total momentum is zero and energies are easier to calculate.

Question 10

A girl of mass $$50\ \mathrm{kg}$$ runs at $$2\ \mathrm{m/s} to $$jump onto a stationary merry-go-round of radius $$5\ \mathrm{m}. $$What is her angular momentum about the center?

Accepted Answer

$$L = 500\ \mathrm{kg\ m^2$/s}$$

Question 11

Which formula gives the angular momentum $$L of a $$point particle moving in a circle of radius $$r$$ with momentum $$p at $$angle $$	heta$$?

Accepted Answer

$$L = rp \sin 	heta$$

Question 12

Newton's Second Law for rotational motion is given by which equation?

Accepted Answer

$$	au = I \alpha$$

Question 13

If the net external torque on a system is zero, what happens to the system's angular momentum?

Accepted Answer

It remains constant.

Question 14

A rotating figure skater pulls in her arms, decreasing her moment of inertia. What happens to her angular speed?

Accepted Answer

It increases.

Question 15

Which equation gives the work done by a torque $$	au$$ over an angular displacement $$\Delta 	heta$$?

Accepted Answer

$$W = 	au \Delta 	heta$$

Question 16

A sphere of mass $$M$$ and radius $$R is $$suspended by a string. A bullet of mass $$m$$ and velocity $$v$$ embeds in the sphere at its center. What is the angular velocity $$\omega of $$the sphere immediately after the collision?

Accepted Answer

$$\omega = \frac{mvR}{I}$$

Question 17

Which rule is used to determine the direction of the angular velocity vector in rotational motion?

Accepted Answer

Right-hand rule

Question 18

A vertical bar of length $$L$$ and mass $$M is $$hinged at one end and released from rest. What principle is used to find the speed of the free end when it hits the ground?

Accepted Answer

Conservation of energy

Question 19

Which of the following is true about gyroscopes and conservation of angular momentum?

Accepted Answer

Gyroscopes are stable because their total angular momentum around any axis is constant.

Momentum, Center of Mass, and Angular Momentum in Introductory Physics

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