Physics 50 Equation Sheet
r
v

v
s
rf
ri
r
t

dr
dt
Us=(1/2)kx2
Elastic PE Function
Average velocity
Emech=K+U
Total Mechanical Energy
Wnc
Instantaneous velocity
Average Speed
t
Average acceleration
v
t


 dv d 2 r
a
dt dt 2
v vo at
a
Instataneous acceleration
x
xo vot (1/ 2)at 2
v2
vo2 2a( x xo )
x
Displacement
Velocity as function of
time
Position as function of
time
Velocity as function of
position
Position as function of
velocity and time
vo v
t
2
xo
v2
ar
r
F ma
w mg
fk
kN
Radial (centripetal)
acceleration
fs
s
Static frictional force
W
F s
Fs
Ws
kx
2
i
(1/ 2)kx
(1/ 2)kx
Kf
Ki
W
t
dW
P
dt
P F v Fv cos
Ug=mgy
Pave=
2
f
Work done by constant
force
Spring force (Hooke’s
Law)
Work done by spring
force
Work done by applied force
Wapplied= - Ws
K=(1/2)mv2
Wnet
P
MV
dP
Fext
dt


I
Fext (t 2


I p2 p1
v2 f
s
(v2i
v1i )
Average angular
acceleration
t
d
dt
o
Impulse due to a constant
net force
Impulse-Momentum
Theorem
Relative velocities in an
elastic collision
Arc length
Average Angular Speed
Instantaneous Angular
Speed
Instantaneous angular
acceleration
d2
dt 2
1 2
t
ot
2
t
Angular position as
function of time
vt
r
Angular speed as function
of time
Angular speed as function
of angular position
Angular position as
function of angular speed
and time
Tangential speed
at
r
Tangential acceleration
o
2
2
o
2 (
o
o
2
Work-Energy Theorem
ar
Average power
I
v2
r
r
mi ri 2
Instantaneous power
Ip
I cm
Instantaneous power
Gravitational PE
Function (constant g)
t1 )

p
t
d
dt
Kinetic energy
K
v1 f
Newton’s 2nd Law
r
Weight of a body
Kinetic friction force
Fs cos
Work by non-conservative
forces
Conservation of
Mechanical Energy
Linear Momentum
U
Ki+Ui = Kf+Uf
Newton’s 2nd Law
N
K
KR

1
I
2
 
r F
I
ext
2
o
t
)
Radial (centripetal)
acceleration
Md 2
Moment of Inertia for
System of Particles
Parallel-Axis Theorem
2
Rotational kinetic energy
Definition of Torque
Newton’s 2nd Law for Rotation
Work Done by a constant
Torque
Work-Energy Theorem for
Rotation
W
W
P
1
I
2
W
t
1
I
2
2
f
2
i
Average power delivered
by Torque
P
K
1
MVcm2
2
vcm
R
a cm
R
L r
L
1
I cm
2
Angular momentum
p
I
dL
dt
Gm1m2
r2
GmM E
Fg
RE
GM E
ext
Fg
wE
g
RE
U
v esc
v
T
E
2
2
Instantaneous power
delivered by Torque
Kinetic Energy =
Translational KE +
Rotational KE
Condition for Rolling
Without Slipping
h
Angular momentum for a
rotating body about axis of
symmetry
Newton’s 2nd Law for
rotation
Newton’s Law of
Gravitation
Weight of a body at surface
of earth
Acceleration of gravity
2
GMm
r
2GM
R
Gravitational Potential
Energy function
GM
r
Circular Orbit Speed
Escape Speed
Orbital Period
4 2 3
r
GM
GMm
2r
1
U
2
Orbital Total Mechanical
Energy