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Classical Mechanics
Kinematics
Laws: none
Definitions:
Position r
Displacement dr
dr
Velocity v 
dt


Acceleration

dv
a
dt

Useful Relations:
Kinematic
Equations
x  x o  v o t  12at 2
v  v o  at
v 2  v o2  2a(x  x o )
x  x o  12 (v  v o )t

Tangential Velocity
2r
vt 

T
Centripetal
Acceleration 
v2
ac 

r
SHM Equations of
Motion
x  A cos( t  
)
v   Asin( t   )
a   2 Acos( t   )
v2   2 (A2  x 2 )
a   2 x
Translation
Rotation
The motion of objects as a whole
The spinning motion of objects
Force
Momentum
Energy
Laws:
Laws:
Laws:
Newton’s Laws
Conservation of
Linear Momentum
Conservation of
Energy
K  U  W nc
1. Law of Inertia
2. F  ma
3. Action/Reaction
Definitions:
Coefficient of
Friction
F

  fr
Fn
Useful Relations:

Mass/weight Rule
Fg  mg

Air Resistance
Fd  bv
Hooke’s Rule
Fs  kx
Law of Gravitation
Fg  G
m m 
1
2
r2
Terminal Speed

mg
vt 
b
Spring  
k
m
Definitions:
Linear Momentum
p  mv
Impulse
J

t

Fdt
Kinematics
Simple Pendulum  
Physical Pendulum  
Definitions:
Work
W  F  ds

Power P 
Torsional Pendulum  

Ip

1. Law of
Rotational Inertia
2.   I
3. Action/Reaction

rectangular plate
1
m(a 2  b 2 )
12

r
mgr
Ip
Laws:
none
Angle 
Angular Disp. d
Angular Velocity
Definitions:

d
Torque   r  F

dt
Rotational Inertia
Angular Acc
I  r 2 dm
d


dt

Useful Relations:
Useful Relations:
Rotational Inertia
Kinematic 
(about cm)
Equations (same)
hoop mr 2
disk 12 mr 2 
Angular/Linear
solid sphere
Rules
2
mr 2

5
s  r
v t  r
 hollow sphere

2
a t  r
mr 2
3
1
a c   2 r 
m 2
rod 12

g
l
Laws:
Definitions:
dW
dt
Kinetic Energy

K  12 mv 2
Useful Relations:  Potential Energy
U  W c
Original 2nd Law

dp 
F 
Useful Relations:
dt
Work-Energy
Impulse/Momentum

Theorem
Theorem
W net  K
p  J
Gravitational
Potential Energy
Ug  mgy or 

mm
U g  G 1 2 
r 
Spring Potential


Energy
U s  12 kx2

0
Center of Mass
rcm  M1
r
dm
Torque

Dot Product
A  B  AB cos   Ax Bx  Ay By  Az Bz

Cross Product A  B  ABsin  n̂
r
A  B  Ay Bz  Az By iˆ  Az Bx  Ax Bz  ĵ  Ax By  Ay Bx k̂




Angular Momentum
Laws:
Conservation of
Angular
Momentum
Definitions:
Angular
Momentum
Lrp

Useful Relations:
Energy
Laws:
Conservation of
Energy (include
rotational kinetic)
K  U  W nc
Useful Relations:
Rotational
Kinetic Energy
K  12 I 2
Angular Momentum
Distributed Object

L  I
Second Law for
Rotation
dL
 
dt
Acceleration due to gravity
g = 9.80 m/s2
Moon - mass: 7.36 x 1022 kg
radius: 1.74 x 106 m
Earth - mass: 5.98 x 1024 kg
radius: 6.38 x 106 m
Earth - moon distance: 3.82 x 108 m
Sun - mass: 1.99 x 1030 kg
radius: 6.96 x 108 m
Sun - Earth distance: 1.50 x 1011 m