Q: A disk rotates with angular velocity $$\omega$$ and angular acceleration $$\alpha. $$Which equation gives the angular position $$\theta as a $$function of time $$t if it $$starts from rest?

$$\theta = \frac{1}{2} \alpha t^2$

Q: A light ray passes from air ($$n_1 = 1.0$) into water (n_2$ = 1.33). $$What is the critical angle $$\theta_c$$ for total internal reflection?

$$\theta_c = \arcsin \left( \frac{n_1$}{n_2$} \right)$$

Question 1

A car accelerates from rest with a constant acceleration $$a$$ for a time $$t. $$Which equation gives the car's displacement $$x$$ during this time?

Accepted Answer

$$x = v_0$ t + \frac{1}{2} a t^2$

Question 2

Which of the following correctly expresses the conservation of energy for a system with kinetic energy $$K$$ and potential energy $$U$$?

Accepted Answer

$$K + U = 	ext{constant}$$

Question 3

A block attached to a spring oscillates with simple harmonic motion. If its position is given by $$x(t) = A \cos(\omega t + \phi)$$, what is the expression for its velocity $$v(t)$$?

Accepted Answer

$$v(t) = -A \omega \sin(\omega t + \phi)$$

Question 4

Which of the following is the correct formula for the moment of inertia $$I of a $$rigid body consisting of $$N$$ point masses $$m_i at $$distances $$r_i$$ from the axis of rotation?

Accepted Answer

$$I = \sum_{i=1}^{N} m_i r_i^2$

Question 5

A wave travels along a string with speed $$v. If $$the frequency of the wave is $$f$$ and the wavelength is $$\lambda$$, which equation relates these quantities?

Accepted Answer

$$v = f \lambda$$

Question 6

A disk rotates with angular velocity $$\omega$$ and angular acceleration $$\alpha. $$Which equation gives the angular position $$	heta as a $$function of time $$t if it $$starts from rest?

Accepted Answer

$$	heta = \frac{1}{2} \alpha t^2$

Question 7

A mass $$m$$ attached to a spring with spring constant $$k$$ oscillates with angular frequency $$\omega. $$What is the correct expression for $$\omega$$?

Accepted Answer

$$\omega = \sqrt{\frac{k}{m}}$$

Question 8

A ball is thrown straight up with initial velocity $$v_0. $$Neglecting air resistance, what is the maximum height $$h$$ reached by the ball?

Accepted Answer

$$h = \frac{v_0$^2}{2g}$$

Question 9

Which of the following correctly describes the condition for constructive interference in a double-slit experiment?

Accepted Answer

$$d \sin 	heta = m \lambda$$

Question 10

A light ray passes from air ($$n_1 = 1.0$) into water (n_2$ = 1.33). $$What is the critical angle $$	heta_c$$ for total internal reflection?

Accepted Answer

$$	heta_c = \arcsin \left( \frac{n_1$}{n_2$} ight)$$

Question 11

A damped oscillator has a solution $$x(t) = A e$$^{-\gamma t}$$ \cos(\omega' t + \phi). $$What does $$\gamma$$ represent physically?

Accepted Answer

The damping coefficient, related to energy loss per cycle

Question 12

A rigid body rotates with angular momentum $$L$$ and moment of inertia $$I. If no $$external torque acts, what happens to $$L$$ and $$I$$?

Accepted Answer

$$L is $$conserved, $$I$$ may change if the body's shape changes

Question 13

A standing wave on a string fixed at both ends has nodes and antinodes. What is the distance between two adjacent nodes?

Accepted Answer

$$\frac{\lambda}{2}$$

Question 14

A point source emits spherical waves. What is the intensity $$I at a $$distance $$r$$ from the source if the power is $$P$$?

Accepted Answer

$$I = \frac{P}{4 \pi r^2$}$$

Question 15

A ball of mass $$m is $$attached to a string and swung in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the tension $$T in $$the string?

Accepted Answer

$$T = \frac{m v^2$}{r}$$

Question 16

A ray of light strikes a plane mirror at an angle of incidence $$	heta. $$What is the angle of reflection?

Accepted Answer

$$	heta$$

Question 17

In a double-slit experiment, what happens to the fringe spacing if the wavelength $$\lambda is $$increased?

Accepted Answer

Fringe spacing increases

Question 18

A pendulum of length $$L$$ swings with small amplitude. What is the period $$T of $$its oscillation?

Accepted Answer

$$T = 2 \pi \sqrt{\frac{L}{g}}$$

Question 19

A lens forms a real image of an object. Which statement is true about the image?

Accepted Answer

The image is inverted and can be projected onto a screen

Physics 163 Final Exam Study Guide: Key Concepts and Equations

Study Guide - Practice Questions

Study Guide - Flashcards