AP Physics C: Mechanics - Table of Information Summary

Constants and Conversion Factors

  • Universal Gravitational Constant (G): G=6.67×10−11m3kg⋅s2=6.67×10−11N⋅m2kg2G = 6.67 \times 10^{-11} \frac{m^3}{kg \cdot s^2} = 6.67 \times 10^{-11} \frac{N \cdot m^2}{kg^2}

  • Acceleration due to Gravity at Earth's Surface (g): g=9.8ms2g = 9.8 \frac{m}{s^2}

  • Magnitude of Gravitational Field Strength at Earth's Surface (g): g=9.8Nkgg = 9.8 \frac{N}{kg}

Prefixes

  • tera: 101210^{12} (T)

  • giga: 10910^9 (G)

  • mega: 10610^6 (M)

  • kilo: 10310^3 (k)

  • centi: 10−210^{-2} (c)

  • milli: 10−310^{-3} (m)

  • micro: 10−610^{-6} ($\mu$)

  • nano: 10−910^{-9} (n)

  • pico: 10−1210^{-12} (p)

Unit Symbols

  • hertz (Hz)

  • newton (N)

  • joule (J)

  • second (s)

  • kilogram (kg)

  • watt (W)

  • meter (m)

Values of Trigonometric Functions for Common Angles

Angle

sin

cos

tan

0∘0^\circ

0

1

0

30∘30^\circ

12\frac{1}{2}

32\frac{\sqrt{3}}{2}

33\frac{\sqrt{3}}{3}

37∘37^\circ

35\frac{3}{5}

45\frac{4}{5}

34\frac{3}{4}

45∘45^\circ

22\frac{\sqrt{2}}{2}

22\frac{\sqrt{2}}{2}

1

53∘53^\circ

45\frac{4}{5}

35\frac{3}{5}

43\frac{4}{3}

60∘60^\circ

32\frac{\sqrt{3}}{2}

12\frac{1}{2}

3\sqrt{3}

90∘90^\circ

1

0

-

Assumptions for the Exam

  • The frame of reference of any problem is assumed to be inertial unless otherwise stated.

  • Air resistance is assumed to be negligible unless otherwise stated.

  • Springs and strings are assumed to be ideal unless otherwise stated.

Mechanics

  • a: acceleration

  • E: energy

  • f: frequency

  • F: force

  • h: height

  • J: impulse

  • k: spring constant

  • K: kinetic energy

  • ℓ: length

  • m: mass

  • M: mass

  • p: momentum

  • P: power

  • r: radius, distance, or position

  • t: time

  • T: period

  • U: potential energy

  • v: velocity or speed

  • W: work

  • x: position or distance

  • y: height

  • l: linear mass density

  • μ\mu: coefficient of friction

  • I: rotational inertia

  • L: angular momentum

  • α\alpha: angular acceleration

  • θ\theta: angle

  • τ\tau: torque

  • ϕ\phi: phase angle

  • ω\omega: angular frequency or angular speed

Geometry and Trigonometry

  • Rectangle: Area A=bhA = bh

  • Triangle: Area A=12bhA = \frac{1}{2}bh

  • Circle: Area A=πr2A = \pi r^2, Circumference C=2πrC = 2 \pi r

  • Rectangular Solid: Volume V=ℓwhV = \ell wh

  • Cylinder: Volume V=πr2hV = \pi r^2 h, Surface Area S=2πrh+2πr2S = 2 \pi r h + 2 \pi r^2

  • Sphere: Volume V=43πr3V = \frac{4}{3} \pi r^3, Surface Area S=4πr2S = 4 \pi r^2

  • Right Triangle:

    • Pythagorean Theorem: a2+b2=c2a^2 + b^2 = c^2

    • sin⁡θ=ac\sin \theta = \frac{a}{c}

    • cos⁡θ=bc\cos \theta = \frac{b}{c}

    • tan⁡θ=ab\tan \theta = \frac{a}{b}

Vectors

Calculus

Identities