Download Formula Sheet File - Eastchester High School

AP Physics formula list
(B1) Ch. 2 Motion in one Dimension
Displacement:
x  x f  xi
Average velocity (all situations):
v
d
t
v
Average velocity (uniform acceleration):
a
Average acceleration:
v f  vi
v
vi  v f
v
t
d
2
1
(v f  vi )t
2
2
Kinematic formulas:
v f  vi  at
d  vi t  ½at 2
v f  vi  2ad
2
2
Kinematic formulas if vi=0:
v f  2ad
2d
a
t
a
2d
t2
Ch. 3 Motion in two Dimensions
x-component
y-component
vix  vi cos
viy  vi sin 
v fx  vix  a x t
v fy  viy  a y t
d x  vixt  ½ a x t 2
d y  viyt  ½a y t 2
v fx  vix  2a x d x
v fy  viy  2a y d y
ax  0
a y  9.8m / s 2 (IF UP IS POSITIVE)
2
2
2
2
(B1) Ch. 4 Laws of Motion
Net force:
 F  ma
Friction equations:
Weight: W  Fg  mg
Static: F f 
 s Fn
x and y components (if θ is to horizontal axis):
Net force using x and y components:
Atwood Machine:
a
Fnet 
( M  m)
g
M m
Kinetic: F f 
Fx  F cos
Fy  F sin 
 F    F 
2
x
 k Fn
2
y
(B1) Ch. 5 Work and Energy
Work: W  F  d  F d cos 
Net work:
Wnet  KE
Total Energy:
Work done against friction: W f   F f d Work done against gravity: Wg  PE  mgh
ET  PE  KE  Q
Total mechanical energy: MEt  KEi  PEi  KE f  PE f = constant
KE  ½mv 2
Kinetic energy:
Gravitational PE: PE  mgh
Elastic PE: PEs  ½kx
2
P
Power Equations:
W Fd mgh


 Fv
t
t
t
(B1) Ch. 6 Momentum and Collisions
Impulse (IS A VECTOR: you will need signs if vf and vi are different directions, or J is opposite direction of motion):
J  p  Ft  mv
p  mv
Momentum:
Conservation of momentum (IS A VECTOR: you will need signs if vf and vi are opposite directions):
m1v1i  m2 v2i  m1v1 f  m2 v2 f
m1  m2 vi  m1v1 f
Explosion:
 m2 v 2 f
p p
Elastic Collision:
i
f
AND:
 KE   KE
i
The perfectly elastic equation (use with conservation of momentum:
p p
Inelastic Collision:
i
f
 KE   KE
i
f
f
v1i  v2i  (v1 f  v2 f )
Q
Perfect Inelastic: m1v1i  m2 v2i  m1  m2 v f (NOTE: This equation is also used to find the v of the center of mass (com). v f is vcom!)
Glancing collisions:
p
ix
  p fx AND:
p
iy
  p fy Note: px  p cos
p y  p sin  (if θ is to the
horizontal!)
Center of mass:
xcm 
m x
m
i i
i
(chose a common origin for all point masses so all positions (all xi and xcm) are relative to that origin.)
(B1) Ch. 7&8 Circular Motion & Torque
Linear velocity for an object moving in a circle: v 
2r
T
v2
Centripetal (radial) acceleration: a c 
r
mv 2
r
Gm1 m2
Gravitational force between two masses: Fg 
r2
Orbital motion:  Frad  Fc  Fg
Centripetal force:
 Frad  Fc  mac 
r 3 Gmcentral
Kepler’s Third Law (Good derivation practice from above 3 equations):

T2
4 2
Pendulum motion/rollercoaster motion:
 Frad  Fc  Fn  Fg  FT  Fg
Acceleration due to gravity:
gp 
(If not at top or bottom of circle, you might have to find components of Fg (if FT is toward center) or find components of FT (If FT is NOT toward center))
Gm p
r2
Gravitational potential energy between two masses: U g  
Gm1m2
r
(This can be used in conservation of energy equation just like mgh)
Escape velocity (a good practice in derivation from conservation of energy using the above equation and ½ mv 2:
Torque:
  F  d  Fd sin 
θ= angle between force and lever arm
Equilibrium:
F

x
net
0
0
F

y
0
cw
  ccw 
v
2Gmp
r
Angular Quantities
Note: Remember all kinematic angular quantities (  ,  , 
) are multiplied by r to get the linear quantity (d,v,a). All Newtonian
Angular quantities (  ,, L ) are divided by r (or r in the case of I) to get the linear quantity (F, m, mv).
2
Angular displacement (1 rev):   s  2r  2
r
r
Angular velocity:  
 2

t t1rev
Angular to linear velocity conversion: v  r
Angular acceleration:


t
Angular to linear acceleration conversion:
at  r
Angular Mass (?) (a.k.a MOMENT OF INERTIA):
Angular Force:

Angular momentum:
 I
L  I  mvr (for orbiting point masses)
Conservation of Angular Momentum:
Angular Impulse(?):
I   mr 2 (β=1 for orbiting point masses)
L  L
L  t
Rotational Kinetic Energy: K rot 
1 2
I
2
i
f
I ii  I f  f
mvi ri  mv f rf
(B2) Ch. 9&10 Fluid Mechanics
Density:

m
v
F
A
F1 F2

A1 A2
Pressure: P 
Hydraulic (Pascal’s) Principle:
Gauge pressure: Pgauge  P  gh
Absolute pressure: Pabs  Pgauge  Patm
Buoyant force: FB  m fluid g   fluidV fluid g
If floating:
F  0  F
B
 Fg (object) (use V of water displaced!)
If sinking or completely submerged:
Continuity equation:
 F  ma  F
Flow rate 
B
 Fg (object) (use V of object!)
V
 A1v2  A2 v2
t
Bernoulli’s equation: P1  ½ v1  gh1  P2  ½ v2  gh2
2
2
(If P1 is higher than P2, and P1=Patm, then P2=Pabs. BUT, If P1 is set to zero, P2=Pgauge)
Torricelli’s equation (STATE IT):
v  2 gh
Note: There could be a third force such as tension or spring force.
(B2) Ch. 12&13 Thermodynamics
L  Lo T
Linear expansion:
H
Rate of heat transfer by conduction:
Q kA

t
L
W  PV
Work done ON a gas:
Internal Energy Equations:
U  Q  W (ΔU=0 for a cycle of a cyclical process since ΔT=0)
3
3
K avg  U  k B T  nRT
2
2
Root mean square velocity: vrms 
Ideal gas equation:
3k BT

PV  nRT  NkBT

3RT
M
Heat engine:
Efficiency equations (%efficiency = e x 100):
Carnot Efficiency:
e
e
Wout Pout

QH
Pin
Wout  QH  QC
TH  TC
TH
(B1) Ch. 14&15 Simple Harmonic Motion (SHM), Vibrations and Waves
Hooke’s Law:
Fs  kx
2
t )  A cos( 2ft )
T
2
t ))  A ( sin( 2ft )) Velocity MAX: vmax  A
Velocity of a system in SHM: v  A (  sin( t ))  A ( sin(
T
Displacement of a system in SHM: x  A cos(t )  A cos(
Acceleration of a system in SHM:
a  A 2 ( cos(t ))  A 2 ( cos(
Period of mass/spring system:
  2
Wave velocity equations:
v  f
v


Wave velocity in a vibrating string:
v
F

Doppler effect: f '  f

V  Vo
V  Vs
m
L
m
k
2
t ))  A 2 ( cos( 2ft )) Thus: amax  A 2
T
Period of pendulum:
  2
L
g
Frequency of standing waves on a string: (at fo, λ=2L)
fn 
nv
n

2L 2L
FT
n = 1,2,3,4…

Frequency of standing waves in air column open: (at fo, λ=2L)
fn 
nv
2L
n = 1,2,3,4…
Frequency of standing waves in air column with 1 closed end: (at fo, λ=4L)
fn 
nv
4L
n = 1,3,5,7…
Consecutive resonances in a variable length air column with 1 closed end vibrating at frequency f: L2  L1 
(B2) Ch. 23 & 24 Light
Index of refraction: n 
c
v
n1 sin 1  n2 sin  2
n
Critical angle: sin  c  int o
n from
Snell’s Law:
(B2) Ch. 26 Diffraction and Thin Films
Double Slit path difference:
  d sin   m
Constructive (mth maxima):
m = 1,2,3,4…
Destructive (mth minima):
m = ½, 3/2, 5/2, 7/2…
Equating θ to X and L:
tan  
X
L
Approximation:

d

X
L
Single Slit Path difference (DESTRUCTIVE, ONLY):
(mth minima): 
 d sin   m m = 1,2,3,4…

2
Thin Film: 2-phase shift
Constructive:
2t= λ
or:
t
m film
2

m0
m=1,2,3…
2n
Destructive:
2t= λ/2
or:
t
m film
4

m0
4n
m=1,3,5…

m0
4n
m=1,3,5…
Soap Bubble: 1-phase shift:
Constructive:
2t= λ/2
or:
t
m film
4
Destructive:
2t= λ
or:
t
m film
2

m0
2n
m=1,2,3…
(B2) Ch. 25 Mirrors and Lenses
Magnification: M 
hi  d i

ho
do
Object/image distance equation:
Lensmakers’ equation: to see that:
1
1
1 
 (n  1)  
f
 R1 R2 
1
1 1
 
do di f
n
1
f
(B1 and B2) Ch. 16&17 Electricity
Force on a point charge:
FE  qE
E
F
q
W  qV
Work done on a point charge:
Get this RIGHT!
or:
V, U, (include sign of charge) E and F (ignore sign) for POINT CHARGE(S):
kq1q 2
r
kq q
F  12 2
r
kq
r
kq
E 2
r
V 
U elec 
k
1
40
V, E, Q and C for PARALLEL PLATES:
V  Ed
Voltage between the plates:
Capacitance equations (If hooked up to a battery: V is constant. If battery is disconnected and capacitor isolated after charging: Q is constant):
C
Q k o A

or Q  VC
V
d
Energy stored in a capacitor:
E  ½CV 2  ½QV
1
1
1
1



 ...
CT C1 C 2 C3
VT  V1  V2  V3  ... QT  Q1  Q2  Q3  ...
Capacitors in series:
Capacitors in parallel:
CT  C1  C2  C3  ...
VT  V1  V2  V3  ... QT  Q1  Q2  Q3  ...
(B1 and B2) Ch. 18&19 Resistors and Circuits
Current: I 
q
t
Resistance: R 
L
Ohms’ Law:
A
V2 W
Power equations:
P  IV  I 2 R 

R
t
Vterm    I T r
Terminal voltage of a battery:
Resistors in series:
RT  R1  R2  R3  ...
VT  V1  V2  V3  ...
I T  I1  I 2  I 3  ...
PT  P1  P2  P3  ...
Resistors in parallel:
1
1
1
1



 ...
RT R1 R2 R3
VT  V1  V2  V3  ...
I T  I1  I 2  I 3  ...
PT  P1  P2  P3  ...
V  IR
(B2) Ch. 20&21 Magnetism
Force on a moving charge in an external B: FB
 qv  B  qvBsin 
mv
qB
FB  IL  B  BIL sin 
FB  FC or: r 
For charge moving in a circular path in external B:
Force on a current-carrying wire in an external B:
B
Strength of B due to a wire:
Flux equation:
 o I 4x10 7 I

2r
2r
  BA cos
 induced 
Induced EMF in a coil:
 n
 I induced R
t
Motional EMF on a straight wire:
 induced  BLv  I induced R
Modern Physics
Energy of a photon: E photon  hf 
Photoelectric Effect:
hc

KEmax  Ei    hf i  hf c
hc
Work function:
  hf c 
KEmax equation:
KEmax  qVs (q=1e)
X-ray emission:
qV  hf max (q=1e)
Compton Effect:
Eincident  KEe  Escattered
Debroglie Wavelength:
Bohr Model:
c
p  mv 
m  m
r
p
or:


 m 1u=931MeV
 1 T1
N  N0   2
2
h
mv
hc
E  mc 2
t
Half Life:

E  Ei  E f  hf 
Equivalence of mass and energy:
Mass defect:
h
c  f