Useful Formulae and Constants
Dot Product
 
A  B  Ax Bx  Ay B y  Az Bz
Rotational Kinematics
1rev  2 rad  360



,  
t
t
  Cross Product
A  B  ( Ay Bz  Az By )iˆ
s   r, v   r , a   r
 ( Az Bx  Ax Bz ) ˆj
 ( Ax B y  Ay Bx )kˆ
f 
1 

T 2
   0  t
1
   0   0 t  t 2
2
 2   20  2   0 
Work, Energy, and Power
 
W  F  d  Fd cos 
1
KE  mv 2
2
PE grav  mgh (near surface)
Mm
(planetary)
R
1
PEelastic  kx 2
2
WNC  KE  PE
 
Energy E
P

 F v
Time
t
PEgrav  G
Rotational Dynamics


Torque:   r  F
magnitude:   rF sin 
direction: right-hand rule
2
I   mi ri , I   r 2 dm
1 2
I (fixed axis)
2
1 2 1
KE  mvcm
 I cm 2 (moving axis)
2
2
 
Angular momentum: L  r  p, L  I
KE 
Momentum and Impulse
p  mv

J  p  Ft   Fdt
Conservation of Momentum
m1 v1  m2 v 2  m1 v1 '  m2 v 2 '
  I
1-Dimensional Elastic Collision
P   
v1  v2  v1 '  v2 '
2