Download AP formula sheet

AP Physics Formulas
1
Topic
Trigonometry
2
Vectors
3
Vectors
sin  
Formulas
adj
cos  hyp
tan  
opp
hyp
opp
adj
R  ( R x ) 2  ( R y ) 2
 
R
  tan 1  R
y
Concept – when to use it
Right triangle trigonometric ratios
Magnitude of resultant vector
Direction of resultant vector
x
v0 v
2
4
Kinematics
5
Kinematics
6
Kinematics
a
9
Kinematics
v  v0  at
10
Kinematics
v 2  v0  2a( x  x0 )
11
Kinematics
x  x0  v0t  12 at 2
12
Kinematics
13
Kinematics
v 2  v0  2 g ( y  y0 )
14
Kinematics
y  y0  v0 yt  12 gt 2
15
Kinematics
x  v0 xt
16
Kinematics
17
Forces
F  ma
Net force resulting in acceleration
18
Forces
W  mg
Weight
19
Forces
f s  s n
Static Friction
20
Forces
f  k n
Kinetic Friction
21
ac 
Centripetal acceleration
25
Circular
Motion
Circular
Motion
Circular
Motion
Circular
Motion
Energy
26
Energy
22
23
24
v
x 
x
t
v0  v
2
v
or
 t
x  x  x0
or
v y  v0 y  gt
2
vo sin 2
g
v2
r
2
v
2r
T
Fc 
mv2
r
W  Fd cos
K  12 mv2
Constant horizontal acceleration given initial and
final velocities and time
Constant horizontal acceleration given initial and
final velocities and a change in horizontal position
Constant horizontal acceleration given initial
velocity, a change in horizontal position, and time
Constant freefall acceleration given initial and final
vertical velocities and time
Constant freefall acceleration given initial and final
vertical velocities and a change in vertical position
Constant freefall acceleration given initial vertical
velocity, a change in vertical position, and time
Horizontal distance of a projectile
Range of a projectile given the initial velocity and
angle of elevation
2
atotal  ac  at
Displacement
Average acceleration
v
t
2
R
Average velocity
2
Total acceleration due to an objects centripetal and
tangential acceleration in non-uniform circular motion
Velocity of an object in uniform circular motion
Net Centripetal force
Work due to a constant force
Kinetic energy
27
Energy
U g  mgh
Gravitational Potential Energy
28
Energy
U e  12 kx2
Elastic Potential energy or work done on a spring
29
Energy
E  K U
Total mechanical energy
30
Energy
Ei  E f
Conservation of mechanical energy (w/o friction)
31
Energy
Ei  E f  W friction
Conservation of mechanical energy (with friction)
32
Energy
Wnet  K f  K i
33
Energy
34
Momentum
p  mv
35
Momentum
I  Ft  mv
36
Momentum
m1v1i  m2 v2i  m1v1 f  m2 v2 f
37
Momentum
m1v1i  m2 v2i  (m1  m2 )v f
38
Momentum
V1i + V1f = V2i +V2f
39
Oscillations
  2f
40
Oscillations
f  T1
41
Oscillations
T
42
Oscillations
T  2
m
k
43
Oscillations
T  2
L
g
44
Oscillations
45
Oscillations
46
Oscillations
47
Oscillations
amax   2 A
48
Rotation
s  r
49
Rotation
v  r
50
Rotation
a  r
51
Rotation
P  Wt
P  Fv
or
k
m


t
or
Impulse due to a force applied over a small
time or due to a change in momentum
Conservation of Momentum – Elastic Collisions
Conservation of Momentum – Inelastic Collisions
Initial and final velocities for two objects
undergoing a completely elastic collision
Angular frequency given the actual frequency
Frequency given the period
Time period given the angular frequency

Time period of a mass oscillating on a spring
Time period of a pendulum of length L
Time period of a physical pendulum
I
mgd
( A2  x 2 )
amax 
Mechanical Power
Linear Momentum
2
T  2
v
Net work due to a change in kinetic energy
kA
m

  0
2
Velocity of an object oscillating in simple harmonic
motion
Maximum acceleration of an oscillating object given
the spring constant
Maximum acceleration of an oscillating object given
the angular frequency
Relationship between arc length and angle
Relationship between tangential (linear) velocity and
angular velocity
Relationship between tangential (linear) acceleration
and angular acceleration
Two formulas for average angular velocity

t
52
Rotation
53
Rotation
   0   0 t  1 2 t 2
54
Rotation
  0  t
55
Rotation
 2  0 2  2
56
Rotation
I   mr 2
57
Rotation
I  mr 2
Moment of inertia (rotational inertia) for a thin hoop
58
Rotation
I  12 mr 2
59
Rotation
I  52 mr 2
60
Rotation
I  121 ML2
61
Rotation
I  13 ML2
62
Rotation
I  I CM  MD 2
Moment of inertia (rotational inertia) for a cylinder
or solid disk
Moment of inertia (rotational inertia) for a solid
sphere
Moment of inertia (rotational inertia) for a uniform
rod rotating about it’s center of mass
Moment of inertia (rotational inertia) for a uniform
rod rotating about it’s endpoint
Parallel-axis theorem
63
Rotation
  F d
64
Rotation
  I
65
Rotation
66
Rotation
P  
67
Rotation
K R  12 I 2
68
Rotation
W  K R
69
Rotation
K  12 I 2  12 mv 2
70
Rotation
L  mvr
Angular momentum for a particle (individual object)
71
Rotation
L  I
Angular momentum for a rigid object
72
Rotation
Li  L f
Conservation of angular momentum
73
Rotation
74
Gravitation
75
Gravitation

Average angular acceleration
Moment of inertia (rotational inertia) for a particle
The torque due to a component of force applied
perpendicular to a lever
Net torque is proportional to its angular acceleration
 cw   ccw
xcm 
 mx
m
and
Fg 
g
ycm 
Gm1m2
r2
Gm
r2
Equation for distance (position) of an object due to
the velocity, acceleration, and time
Equation for the final velocity due to an initial
velocity, acceleration, and time
Equation for the final angular velocity due to an
initial velocity, acceleration, & angular position
Rotational equilibrium-clockwise and
counterclockwise torques are balanced
Power delivered to a rotating rigid object
Rotational kinetic energy
Work-kinetic energy theorem for rotational motion
 my
m
Total kinetic energy of a rolling object
X and Y components for an object’s center of mass
Newton’s Law of Universal Gravitation
(Gravitation Force)
Acceleration due to gravity given planet’s mass
radius
g
76
Gravitation
77
Gravitation
U   Gmr1m2
78
Orbits
 r
T 2  4GM
79
Orbits
E  12 mv2  Gmr1m2
80
Orbits
E   GMm
2r
Total energy for circular orbits
81
Orbits
E   GMm
2a
Total energy for elliptical orbits
82
Orbits
Gm
( r h)2
2 3
vesc 
2 GM
R
Acceleration due to gravity at a certain altitude.
Gravitational Potential energy given two masses and
the distance between them
Kepler’s 3rd Law
Total energy of an orbiting body
Escape velocity given “planet’s” mass and radius