Physics Exam Equation Sheet
1D Kinematics
2D Kinematics
Quadratic Formula
x = vo t + ½ a t2
x = vox t + ½ ax t2
y = voy t + ½ ay t2
a t2 + b t + c = 0
vx = vox + ax t
vy = voy + ay t
t
v = vo + a t
v2 = vo2 + 2 a x
 b  b 2  4ac
2a
vx2 = vox2 + 2 ax x
vy2 = voy2 + 2 ay y
Forces
Work and Energy
ΣFx = m ax
ΣFy = m ay
ΣFr = m ac & ac = v2/r
W=Fd
W = ½ k x2
W = ΔKE
(work)
(spring work)
ΔPE + ΔKE = O
ΔPE + ΔKE = Wnc
ΔPE= PEf – PEo
ΔKE = KEf – KEo
Ef - Eo = Wnc
Ef = Eo
E = KE + PE
PE = m g h
KE = ½ m v2
PE = ½ k x2
(ideal)
(with losses)
W=mg
Ff = μ N
Fs = -k (x-xo)
F = k (x-xo)
(weight)
(friction)
(from spring)
(applied on a
spring)
Power
P=W/t
P=F v
(linear)
(linear)
P = τ
(rotational)
Hp = τ n / 63025 (τ in inlb)
kW = τ n / 9550 (τ in Nm)
(with losses)
(ideal)
(height)
(velocity)
(springs)
Rotational Kinematics
Rotational Dynamics
Power Drives
θ = ωo t + ½ α t2
ω = ωo + α t
ω2 = ωo2 + 2 α θ
ac = r ω2
at = r α
vt = r ω = 2πr/T
s=rθ
τ=rF
Στ = 0
Στ = I α
τ 1/t1 = τ 2/t2
f = 1/T
ω = 2πf
(T is period)
(τ is torque)
Wr = τ θ
KEr = ½ I ω2
Etot=½ m v2 + ½ I ω2 + mgh
L=Iω
ΔL = 0
ΔL = Lf – Lo
(τ is torque &
t is # of teeth)
(equilibrium)
(motion)
(angular
momentum)
(gears and chains)
t1 ω1 = t2 ω2
t1 n1 = t2 n2
τ 1/r1 = τ 2/r2 (belts)
r1 ω1 = r2 ω2
r1 n1 = r2 n2
Physics Exam Equation Sheet
Linear Momentum
SHM
ΔP = 0
ΔP = Pf – Po
x = A cos ( ω t )
v = - A ω sin ( ω t )
a = - A ω2 cos ( ω t ) = - ω2 x
p=mv
impulse = F Δt = m vf – m vo
 m  m2 
 v o1
v f1   1
m

m
2 
 1
 2m1 
 v o1
v f2  
 m1  m 2 
elastic
collision
& vo2 = 0
f = 1/T
ω = 2πf
ω
k
m
v
k 2
(A  x 2 )
m
E = ½ k x2
Center of Mass
Xcm 
m x
m
i
i
i
Sound
I=P/A
I = P / 4 π r2 (point source)
β = (10dB) log (I /Io) where Io = 1x10-12
from math... y = 10 x & x = log 10 y
(T is period)
(mass on spring)