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Linear Kinematics:
x
= (vf + vi)/2
V
t
vectors: never mix x and y
dx
1
v
x  v 0t  at 2 ,
dt
2
1
x  v f t  at 2
2

v
,
a
t

1
x  v 0  v f t note: this is just average speed x time
2


x( or distance traveled) = ∫ v dt = area under a speed vs time graph
dv
= slope of a velocity vs time graph
a
dt


Dynamics
Σ F  ma,
Ff  FN




v 2f  v 02  2ax
Range equation: R = 2V o 2 (sin 2φ)/g = horizontal distance traveled if shot at angle


d2x
a 2
 dt
Fg  
G
vectors: never mix x and y
ixj=k
w  mg
but against circle j x i = -k
( s is a maximum therefore can be less than calculated, and k is constant)
m1m2
r2
Fc  mac ,
Fc  m
v2
,
r
Fs  kx





scalars. Direction is less important….easier……very little trig.
Dot product yields scalar projections: i∙i = 1, i∙j = 0
Energy:
W  F  d  Fd cos , W   Fdxcos = area under an F vs distance graph
W  K , W  U
U g  mgh on a planet,
mm
Ug  G 1 2 between objects (like Earth and Sun, apple and moon)

 r
1 2
K   mv
2
Total Mechanical Energy E = K + U
For satellites in circular orbit
Fc =Fg to find orbital velocity
U = K to find escape velocity
K = -U/2 and E = -GMm/2r where are is the separation between centers
U i  Ki  U f  K f
if gravity is the only force in play
1
Us  kx2
2
F = -dU/dx = negative of slope on a U vs x graph.

Know shapes of stable, unstable and neutral equilibrium.
W
= dU/dt
t
P  Fv used mainly when sliding an object against friction at constant speed
P
Momentum vectors again; separate x and y

dp
= slope of a momentum vs time graph
p  mv , pi  p f , F 
dt
J  mv , J  Ft , J   Fdt = area under an F vs t graph



 & Oscillation
Rotation


2π radians = 360°

,

t

1
   0 t  t 2
2 




,
t

v  r
s  r
d
dt

at  r
d

dt

1
   i   f t
2

Fc  m 2 r
CM calculation: Pick a convenient origin then do
 z
Xcm = Σmx/Σm. Next do y and


If there is no outside force acting, the motion of the CM will remain unchanged.
If an outside force is acting, F =ma find the acceleration of the CM.
If you are rotating about the CM
Other shapes
us I 
 r dm,
2
I   mr 2
Ihoop = mr2
I disk = ½ mr2
I   r 2dV
(called a volume integral if you did it in calculus)
If you are rotating about any axis a distance d from the center of mass

I p  Icm  
Md 2

1
K r  I 2
2
L  I ,





  I ,
  rF sin  = rxF (RHR for direction)
L  mvrsin 


Kepler: for any satellite about a central star
4 2
T
, (k goes to 1 when AU’s and Years are used)
2  ksa 3 , k s 
Gms
l
m
Tp  2
Ts  2
g
k

I
for the rocking oscillation of any shape of known I
mgd 
2r
2
x  Acost    where A is the amplitude. (or use sine)
v

T
T
d2x
a   A 2 cost    , a  2 , a   2 x
v  dx / dt   A sin t    ,
dt


Tcp  2