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Physics Equations
1 Mechanics
1.1 Dimensional motion
~v = ~v o
x = xo +
(~v + ~vo)t
x = xo + ~vot +
~at
2
x = xo + ~vt −
~at
2
~v
2
= ~v
2
o
~r AB
= ~r A
− ~r B
x : Distance, m
xo : Initial distance, starting point, m
~v : Velocity, ms
− 1
~v o
: Initial velocity, ms
− 1
t : Time, s
~a : Acceleration, ms
− 2
~rAB : Position of
A relative to
B
~r V
: Position of
V realtive to origin
1.2 Conversions
km · h
− 1 −→ m · s
− 1
Multiply by
5 / 18
m · s
− 1 −→ km · h
− 1
Multiply by
18 / 5
1.3 Projectile motion
vy = vy o
− gt
x = x o
t
y = yo + vy o
t −
gt
2
y = x tan θ −
g
x
vo cos θ
2
y max
v
2
o
sin
2 θ
2 g
x max
v
2
o
sin 2θ
g
tmax =
2 v o
sin θ
g
y : Graph of the trajectory
t : Time
y max
: Maximum y-coord reached by projectile
x max
: Maximum x-coord reached by projectile
t max
: Time for which projectile airborne
1.4 Circular motion
~ac =
v
2
r
4 π
2 r
T
2
T =
2 πr
v
f
~ac : Cetripetal acceleration
T : Period of uniform circular motion
f : Frequency, number of revolutions per unit time
r : Radius of circle
2 Forces
P = m~v
F = m~a
F
g
= m~g
F
sp
= −kx
P =
F ∆t = m∆~v = J
F : Force, N = kg · ms
− 1
F
g
: Gravitational force, kg · m
2 s
− 2
m : Mass, kg
~g : Gravity, − 9. 81 · kg · ms
− 2
Fsp : Spring force, N
k : Spring constant, N m
− 1 = kg · m
− 2 s
− 2
P : Momentum, kg · ms
− 1
J : Impulse
2.1 Friction
f s
6 μ s
F
N
fk = μk
FN
f i
: Force of static (i = s) or kinetic (i = k) friction
μi : Coefficient of static (i = s) or kinetic (i = k) friction
F
N
: Normal force
3 Energy
Ek =
mv
2
EGP = mg∆h
E
EP
kx
2
E
k
: Kinetic energy
EGP : Gravitational potential energy
E
EP
: Elastic potential energy
3.1 Work and Power
A •
B = cos θ|A||B| =
Ax
Bx +
Ay
By
W =
F • ∆~r
W =
x 2
x 1
f (x)dx
W =
~r 2
~r 1
F • ∆~r (line integral)
∆E
k
= W
net
P =
∆W
∆t
P =
F • ~v
∆EGP
ab
b
a
F • ∆~r
A •
B : Dot product of vectors
A and
B
|A| : Magnitude, length of vector
A
Ax : x-parameter of vector
A
W : Work, J = kg · m
2 s
− 1
P : Power, W = kg · m
2 s
− 2
3.2 Torque
τ = r
F sin θ
~τ = ~r ×
F
τ = Iα
τ : Torque, N m
I : Rotational inertia
α : Angular acceleration
