Q: Which of the following correctly expresses the angular momentum $$\vec{L} of a $$particle of mass $$m$$ moving with velocity $$\vec{v} at $$position $$\vec{r}$$ relative to the origin?

$$\vec{L} = \vec{r} \times m\vec{v}$$

Question 1

An ice skater spins with arms extended and then pulls her arms in close to her body. Which of the following statements best explains what happens to her angular velocity, assuming no external torques act on her?

Accepted Answer

Her angular velocity increases because her moment of inertia decreases.

Question 2

A powered toy car is initially at rest on a track with no external torque in the horizontal plane. When the car starts to accelerate, what happens to the angular velocity of the track?

Accepted Answer

It rotates in the opposite direction to the car.

Question 3

Which of the following correctly expresses the angular momentum $$\vec{L} of a $$particle of mass $$m$$ moving with velocity $$\vec{v} at $$position $$\vec{r}$$ relative to the origin?

Accepted Answer

$$\vec{L} = \vec{r} 	imes m\vec{v}$$

Question 4

Two ice skaters of equal mass $$m$$ collide inelastically and grab each other, rotating about their combined center of mass. If each skater was moving at speed $$v$$ before the collision, what is the magnitude of their total angular momentum after the collision (assuming their radii are negligible)?

Accepted Answer

$$L = 2mvr$$

Question 5

A mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates with negligible friction. What is the period $$T of $$the oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Question 6

A vertical spring supports a mass $$m. $$What is the equilibrium displacement $$y_0$$ from the unstretched position due to gravity?

Accepted Answer

$$y_0$$ = \frac{mg}{k}$$

Question 7

For a simple pendulum of length $$L$$ and small amplitude, what is the angular frequency $$\omega of $$its oscillation?

Accepted Answer

$$\omega = \sqrt{g/L}$$

Question 8

A physical pendulum consists of a uniform rod of length $$L$$ and mass $$m$$ pivoted at one end. What is the expression for its period for small oscillations?

Accepted Answer

$$T = 2\pi \sqrt{\frac{I}{mgd}}$$

Question 9

Which of the following is the general solution to the wave equation $$\frac{\$$partial^2$$ y}{\partial x^2$} = \frac{1}{v^2$} \frac{\$$partial^2$$ y}{\partial t^2$}$$ for a wave traveling in the positive $$x-$$direction?

Accepted Answer

$$y(x,t) = A \sin(kx - \omega t + \phi)$$

Question 10

A string of length $$L is $$fixed at both ends. What is the wavelength $$\lambda_n of $$the $$nth $$harmonic standing wave?

Accepted Answer

$$\lambda_n = \frac{2L}{n}$$

Question 11

You replace a hanging mass $$m$$ with $$4m on a $$wire of length $$L to $$study standing waves. What happens to the frequency and wavelength of the fundamental mode?

Accepted Answer

Frequency doubles, wavelength unchanged.

Question 12

A sound wave in air is described by the displacement $$s(x,t). At $$what point in the wave is the pressure maximum relative to the displacement?

Accepted Answer

A quarter period out of phase with the displacement.

Question 13

A tube is closed at one end and open at the other. What is the wavelength of the fundamental mode?

Accepted Answer

$$\lambda = 4L$$

Question 14

A stationary observer hears a higher pitch from an approaching ambulance. Which effect explains this observation?

Accepted Answer

Doppler effect

Question 15

A source emits sound at frequency $$f_0$$ and moves toward a stationary observer at speed $$v_s. $$What is the frequency $$f$$ heard by the observer?

Accepted Answer

$$f = f_0$ \frac{v}{v - v_s}$$

Question 16

Which of the following is the correct expression for the relativistic kinetic energy $$K of a $$particle of mass $$m$$ moving at speed $$v$$?

Accepted Answer

$$K = (\gamma - 1)mc^2$

Question 17

A muon travels toward Earth at a speed such that $$\gamma = 100. If $$its proper lifetime is $$2.2\ \mu s$$, what is its observed lifetime in Earth's frame?

Accepted Answer

$$220\ \mu s$$

Question 18

According to special relativity, how does the length $$L' of an $$object moving at speed $$v$$ compare to its proper length $$L$$?

Accepted Answer

$$L' = L/\gamma$$

Physics 211: Angular Momentum, Simple Harmonic Motion, Waves, Sound, and Special Relativity

Study Guide - Practice Questions

Study Guide - Flashcards