Useful Equations:
Physics 202
FORCE and MOMENTUM:


Momentum: p  mv (and p is conserved in the absence of external forces)
Force:
2nd law:
dp
 F  dt
 F  ma
or
(if mass is constant)
3rd law: FAB   FBA
Impulse: Impulse   F dt
and
 F dt  p
ENERGY:
Kinetic Energy:
Work:

kg m 2 
1 J  1 2 
s 

K  2 mv 2
1
work   F  dx  F  x (if force is constant)
 
Work-energy theorem: Net work   F  dx  K
Gravity:


F  mg (pointing down),
U  mgh


F   kx ,
U  2 kx 2
Ideal Springs:
1
CONSERVATIVE FORCES:
Let FU  FU , x iˆ  FU , y ˆj  FU , z kˆ



dU
dU
dU
Then FU , x  
, FU , y  
, and FU , z  
dx
dz
dy
And U    FU  dx
Physics 202 equations
Page 2
ROTATION:
If angular acceleration is constant,
  0t  12  t 2
 
1
2
0    t
Rotational Inertia: I   m r 2
 (t )  0   t
,
1
2
 2f  12 i2      
and for a rolling object I   M R2
2
Parallel axis theorem: 𝐼𝑎𝑏𝑜𝑢𝑡 𝑎𝑛𝑦 𝑝𝑜𝑖𝑛𝑡 = 𝐼𝑎𝑏𝑜𝑢𝑡 𝑡ℎ𝑒 𝐶𝑀 + 𝑀𝑅𝐶𝑀
Kinetic Energy:
Ktranslation  12 m v2
Work: Work    d
Angular momentum:
or
and
Krotation  12 I  2
Work    if torque is constant
 I  (for a rigid body) or
 r  p (always)
Torque:   r  F
if I is constant
   I 

Newton’s second law: 
d
d
  r  p  (always)
  
dt dt

FLUIDS:
Flow rate: flow rate 
volume
 velocity  Area
time
or
 v dA
Static Fluid Pressure: P   g depth
if  is constant
U
 P g y
Fluid Potential: fluid potential  P 
vol.
if  is constant
Bernoulli’s equation (in the absence of friction):
K
P
 constant OR P   g y  12  v2  constant
vol.
Fd

kinematic viscosity   
Viscosity:  
Av

Viscosity controlled flow:
 potential difference   flow rate   resistance
Poisuille’s equation (hollow pipes): resistance=
8
 r4

 length, r  radius 
Darcy’s equation (flow through materials):

resistance=
   kinematic viscosity,  length,   permeability 
  Area
Physics 202 equations
Page 3
ELECTRIC FORCES, FIELDS, AND POTENTIALS:
Coulomb’s Law and Electric Fields:
The magnitude of the force between point charges separated by a distance r is given by
k q q  1  q1 q2
F  12 2  

2
r
 4 0  r
 
The electric field is the force per unit charge, F  q E .
For a point charge the magnitude is given by
kq
E 2
r
Electric Potential:
The electric potential V is the potential energy per unit charge:
dV
dV
and
V    E  dx ,
Ex  
, Ey  
, etc.
dx
dy
If we choose to set the potential of points infinitely far from charges to be zero, then the
potential of a point charge is given by:
kq  1  q
V


r
 4 0  r
ELECTRIC CIRCUITS:
V  IR
Resistors (Ohm’s Law):
Power:
Power  V I  I 2 R
Kirchhoff’s Rules:
1. “Current in = current out” or “  Iin  0 ”
2. Going around a closed loop,
Resistors in parallel:
1
RTOTAL

 voltages  0
1
1

 
R1 R2
RTOTAL  R1  R2  
…in
series: