Download Equation List – AP Physics B

Equation List – AP Physics C, Mechanics
Kinematics/Rotational Kinematics
Equivalent variables: x and θ; v and ω; a and ά
Kinematics
x
v
t
a
v
t
Rotational Kinematics


t


t
x 
1
(vi  vf )t
2
1
x  vit  a(t ) 2
2
 
1
(i  f )t
2
1
  it   (t ) 2
2
vf  vi  at
f  i  t
vf 2  vi 2  2ax
f 2  i 2  2
Translating between rotational and linear kinematics
vT  r
tangential velocity
aT  r
tangential acceleration
ac 
vT2
 r 2
r
centripetal acceleration
Equation List – AP Physics C, Mechanics
Newton’s Laws and gravitation
Newton’s 3 laws
1. An object at rest will stay at rest and an object in motion will stay in motion along
a straight-line path, until acted upon by an outside force.
2.  F  ma .
3. For every action, there is an equal and opposite reaction.
Gravitation
Gm1m 2
r2
F
W  mg
Weight of an object, in Newtons
Since W also equals
g
GmE
r2
v
2r
T
Force of gravitational attraction between 2 objects
GmEm
, where mE is the mass of earth, it is readily seen that
r2
velocity of a satellite in circular orbit, with period T
Fc 
mv 2
r
centripetal force on an orbiting satellite
v
GmE
r
velocity of a satellite in circular orbit
v
2GmE
 2 grE
rE
satellite escape velocity
T
2r
U (r ) 
3
2
GmE
 Gm1m 2
r
period of a satellite in circular orbit
gravitational potential energy; U=0 at r=∞
Equation List – AP Physics C, Mechanics
Work, Power, Conservation of Energy
A  B  AB cos 
W  ( F cos  )x  KE
KE 
1 2
mv
2
Work/Kinetic energy theorem
Kinetic energy
1
1
1
1
m1v12i  m 2v22i  m1v12f  m 2v22 f
2
2
2
2
Conservation of kinetic energy for a
perfectly elastic collision
PEg  mgh
Gravitational potential energy (close to earth)
F  kx
Force on a spring
PEs 
P
1 2
kx
2
W
t
Emech  KE  PE  constant
Elastic (spring) potential energy
Power
Conservation of mechanical energy, no friction
Friction
fs max  sFN
static friction
fk  kFN
kinetic friction
Equation List – AP Physics C, Mechanics
Momentum
p  mv
momentum
Ft  p
Impulse momentum theorem
m1v1i  m2v 2i  m1v1 f  m2v 2 f
Conservation of momentum
m1v1i  m2v 2i  (m1  m2)vf
Conservation of momentum for a perfectly inelastic
collision
Center of mass
xcm 
m1 x1  m 2 x 2
m1  m 2
location of center of mass
vcm 
m1v1  m 2v 2
m1  m 2
velocity of center of mass
Equation List – AP Physics C, Mechanics
Rotational Dynamics and Their Linear Equivalents
  FL sin 
Torque
I  mL2
Moment of inertia
I  Icm  mh 2
Parallel axis theorem
Rotational Equation
Linear Equivalent
τ torque
F force
I moment of inertia
m mass
ά angular acceleration
a linear acceleration

A X B  AB sin  n
cross product of two vectors
L  I  mvr sin  momentum
p  mv momentum
KEr 
1 2
I
2
  I 
dL
dt
KE 
1 2
mv
2
dp
 F  ma  dt
Wr   work
W  Fx work
P  
P  Fv
Equation List – AP Physics C, Mechanics
Simple Harmonic Motion
f 
1
T
frequency, cycles/s or Hz
  t

2
 2f
T
angular displacement, radians
angular frequency, rad/s

k 2
m
; T  2

m T
k
spring

L
g 2
; T  2

g
L
T
pendulum

I
MgD 2
; T  2

MgD
I
T
physical pendulum
x  A cos(t   )
v   A sin( t   )
v max  A
vmax occurs where
sin(ώt)=1
a   A 2 cos(t   )   2 x
a max  A 2
amax occurs where
cos(ώt)=1
Elasticity
L 1 F

L Y A
Young’s modulus
x 1 F

 tan 
L
S A
Shear modulus
Equation List – AP Physics C, E&M
Electric fields / electric charge
F
kq1q 2
r2
Coulomb’s law
E
F kq

q0 r 2
Electric field strength
E
q
 V


 0A  0 d
Parallel plate capacitor
 En dA 
Qinside
0
Gauss’s law for a point charge
V 
EPE
q0
EPE – electrical potential energy
V 
kq
r
Potential of a point charge
E
V
s
Electric field strength, volts/meter
q  CV
C
charge on a capacitor
k 0 A
d
Energy 
capacitance, parallel plate capacitor
1
CV 2
2
Energy of a capacitor
Equation List – AP Physics C, E&M
Voltage / Current / Resistance / Capacitance
I
q
t
Definition of electrical current
V  IR
P  IV  I 2 R 
Voltage
V2
R
Electrical power
Rs  R1  R2  ...
Resistors in series
1
1
1
 
 ...
Rp R1 R 2
Resistors in parallel
Cp  C1  C 2  ...
Capacitors in parallel
1
1
1


 ...
Cp C1 C 2
Capacitors in series

q  q0 1  e t /( RC)
q  q 0e t /( RC )

Capacitor charging
Capacitor discharging
Equation List – AP Physics C, E&M
Magnetism
F  qv  B
Magnetic force on a moving charge
 

dF  Idl  B
Magnetic force on a current element
B
 0 qv  r
4 r 2
B due to a moving point charge

 Idl  r
dB  0
4 r 2
Biot-Savart law
0
2R 2 I
Bx 
4 ( x 2  R 2 ) 3 / 2
B on the axis of a current loop
B   0 nI
Inside a solenoid, no end effects
B
 0 2I
4 r
Infinitely long, straight wire
dF12  0 I 1 I 2

dl
2R
B
0 I
r r  R;
2R 2
B
 0 NI
2r
Force/unit length for parallel conducting wires
B
0 I
2r
rR
Inside a toroid
B inside/outside a conductor
Equation List – AP Physics C, E&M
Magnetism
m   Bn dA
S
 
d m
dt
Magnetic flux
Faraday’s law
  vBl
Motional emf
 m  LI
Self inductance
Um 
1 2
LI
2
Energy stored in an inductor