Kinematics equations in 2-D (assume to=0)

dr 
v
dt


d 2 r dv 

a
dt
dt 2
For a constant we get :
  
1
r  ro  vo t  at 2
2
2
2
vi  voi  2ai (ri  roi )
  
v  vo  a t
where i  x or y
Newton’s Laws of Motion
1st. Objects have inertia.


2nd.
F  ma , the net force on a body causes acceleration.


3rd. FAB   FBA , 3rd law pairs do not act on the same body.

Static Friction :
f s,m ax   s N
Kinetic Friction :
f k  k N
Springs : Hooke' s Law
F  -kx
Circular Motion:
Centripetal Acceleration :
2
vt
r
In order to move in a circle needs sum of forces on body to equal :
 F  ma c
ac 
Tangential Acceleration and Velocity :
s  r
ds
 v t  r
dt
d 2s
 a t  r
dt 2
Angular Kinematics Equations
   o  t
 2   o  2 (   o )
2
1
2
   o   o t  t 2
Momentum and Impulse


p  mv


dp
Fn et 
dt
Impulse


Ft  p
In collisions with no external force :

Fn et  0,


p f  po