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A collection of equations and formulas for various physics concepts covered in a university-level physics 131 course during the fall 2007 semester. Topics include kinematics, forces and potentials, work-energy, systems of particles, rotation, electric force and potential energy, vectors, and mathematics. This equation sheet can be used as a study aid for exam preparation.
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Phys 131 Equation Sheet Fall 2007
Kinematics: v = v 0
at x = x 0
v 0
t +
at
2
v
2
= v
2
0
) a rad
v
2
r
~v P/A
= ~v P/B
Forces and Potentials:
d~p
dt
f r,s
≤ μ s
N
f r,k
= μ k
N
s
= −k(x − x R
s
k(x − x R
2 ~ F g
r
2
rˆ U g
r
2
=
4 π
2 r
3
Work-Energy: W =
∫ r 2
r 1
F · d~r W =
F · ~r Ki + Wtot = Kf P =
F · ~v
∫ B
A
F · d~r Fx = −
dU
dx
Systems of Particles: ~p = m~v
d~p
dt
M x cm
= m 1
x 1
x 2
∑
i
m i
x i
∑
ext
= M~a c
m v 2 f
− v 1 f
= −(v 2 i
− v i 1
Rotation: θ = θ 0
t +
αt
2 ω = ω 0
2 = ω
2
0
) v = ωr
a tan
= αr a rad
= ω
2 r
L = ~r × p~ (particle) L = Iω (rigid body) ~τ = ~r ×
∑
i
mir
2
i
Iω
2
∑
~τext =
d
dt
∑
τext = Iα I = Icm + M d
2
2
cm
cm
ω
2
Electric Force and Potential Energy:
F = k
q 1
q 2
r
2
rˆ U = k
q 1
q 2
r
Vectors: Ax = A cos θ Ay = A sin θ A =
√
2
x
2
y
B = AB cos φAB
x
x
y
y
z
z
B = ˆnAB sin φ AB
Math: ax
2
−b ±
b
2 − 4 ac
2 a
(1 + x)
n ≈ 1 + nx for x 1
Constants: g = 9.8m/s
2 G = 6. 67 × 10
− 11 Nm
2 /kg
2 R Earth
6 m
MEarth = 5. 98 × 10
24
kg MSun = 1. 99 × 10
30
kg c = 2. 998 × 10
8
m/s
e = 1. 602 × 10
− 19 C k = 1/ 4 π 0
9 Nm
2 /C
2
− 12
C
2
/Nm
2
me = 9. 109 × 10
− 31
kg