Formulas Flashcards
1
Q
Power
A
Rate of work done
Power= Work/time Unit: Watt
2
Q
Efficiency of Work
A
Work_out/Energy_in
3
Q
Heating a solid, liquid, or gas formula
A
Q= m c ΔT c= specific heat Q= heat added
4
Q
Linear Momentum
A
p=mv
Momentum is conserved in collisions
5
Q
Centre of Mass
A
Point masses on a line
x_cm= Sum of (mx)/M_total
6
Q
Pressure under Water
A
P= p g h p = density of water h= dept of water
7
Q
Universal Gravitation
A
F= G (mm/r^2) G= 6.67 x 10^-11 N m^2/kg^2
8
Q
Mechanical energy
A
PE_grav= P = mgh KE_linear= K = 1/2mv^2
9
Q
Snell’s Law
A
n1sinθ=n2sin θ
10
Q
Index of refraction
A
n=c/v
c= speed of light 3 x 10^8 m/s
11
Q
Periodic Waves
A
v= f λ f= 1/T T = period of wave
12
Q
Bouyant Force
A
Fb= p V g = (m_displaced fluid)g = weight_displaced fluid p= density of the fluid V= Volume of the fluid
13
Q
Ohm’s Law
A
V= IR V= Voltage I= current R= resistance
14
Q
Resistance of a Wire
A
R= p L / A_x p= resistivity of wire material L= length of the wire A_x= cross sectional area
15
Q
Heat of a phase change
A
Q= m L L= latent heat of phase change
16
Q
Hooke’s Law
A
F= k x
PE of spring
W= 1/2kx^2 = work done on spring
17
Q
Electric Power
A
P = I^2R = V^2/R= IV
18
Q
Speed of wave on string
A
T = mv^2/L T = tension in string m = mass of string L = length of string
19
Q
Projectile Motion
A
Horizontal: x-x_o = v_o t + 0
Vertical: y-y_o = v+o t + 1/2at^2
20
Q
Centripetal Force
A
F= mv^2/r = mw^2r
21
Q
Kirchhoff’s Law
A
Loop Rule: Sum_around any loop Δ V_i=0
Node rule: Sym_at any node I_i=0
22
Q
Minimum speed at the top of a Vertical circular loop
A
v=Sqrt(rg)
23
Q
Resistor Combos
A
Series: R_eq= R1+R2+R3….
Parallel = 1/R_eq
24
Q
Newton’s second law and Rotation Inertia
A
τ = torque = I α I = moment of inertia = m r^2
25
Circular unbanked tracks
mv^2/r = umg
26
Continuity of fluid flow
A_in v_in = A_out v_out
A = Area
v= velocity
27
Moment of Inertia
```
Cylindrical hoop: m r^2 para to hoop
Solid cylinder or disk: 1/2 m^2 para to disk
Sold sphere: 2/5 m r^2
hollow sphere: 2/3m r^2
Thin rod center: 1/12 m L^2 para to rod
Thin rod end 1/3 m L^2 para to rod
```
28
Capacitors
```
Q= CV
Q= charge on capacitor
C= Capacitance
V= voltage applied
```
29
Charging a capacitor
```
I(t) = I_o e ^(-t/RC)
Q(t) = Q_o e (1-e^(-t/RC))
e = 2.718
t = time since circuit change
R = resistance (Ohm)
C = capacitance (farad)
```
30
Ohm
Volt/amp
31
Farad
Coulomb/ Volt
32
Thermal Expansion
Linear: ΔL = L_o alpha ΔT
Volume: ΔV = V_o beta ΔT
33
Bernoulli's Equation
P + p g h+ 1/2 pv^2= constant
| Q_Volume Flow Rate= A1v1 = A2v2= constant
34
Rotational KE
KE_rotational = 1/2 I w^2 = 1/2 I (v/r)^2
| KE_ rolling w/o slipping = 1/2 mv^2 + 1/2 I w^2
35
Angular Momentum = L
L= I w= m v r sin θ
Angular impulse equals change in Angular momentum
ΔL= torque Δt= Δ(I w)
36
Period of Simple Harmonic Motion
```
T = 2 pi sqrt(m/k)
k = spring constant
f = 1/T = 1/period
```
37
Banked Circular tracks
v^2 = r g tan θ
38
First Law of Thermodynamics
ΔU = Qnet + W net
Change in Internal Energy of a system =
+ Net Heat added to the system
+ Work done on the system
39
Flower of Heat through a Solid
```
ΔQ/Δt = (k A ΔT)/ L
k = thermal conductivity
A = area of solid
L = thickness of solid
```
40
PE stored in Capacitor
P = 1/2 C V^2
41
RC Circuit Formula (Charging)
V_e = V_cell (1-e^(-t/RC))
RC = time constant
V_cell- V_capacitor - IR = 0
42
Simple Pendulum
```
T = 2pi sqrt (L/g)
f = 1/T
```
43
Sinusoidal motion
```
x= A cos (wt) = A cos (2pi f t)
w= angular frequency
f= frequency
```
44
Doppler Effect
```
f' = f (343 (+_) v_o)/(343 (_+) v_s)
v_o= velocity of observer
v_s= velocity of source
```
45
2nd Law of Thermodynamics
Change in internal energy of system is ΔU = Q added + W done on - Q lost - W done by
46
Thin lens equation
```
1/f = 1/D_o + 1/D_i= 1/o +1/i
f = focal length
i = image distance
o = object distance
Magnification: M = -D_i/D_o =
-i/o = H_i/H_o
```
47
Mirrors and Lens: Positive focal length
```
Mirror : concave
Lens: converging
Object distance o = all objects
Object height H_o= all objects
Image distance = i real
Image height = H_i virtual;upright
Magnification : Virtual; upright
```
48
Mirrors and lens: Negative focal length
```
Mirror : convex
Lens: diverging
Object distance o = all objects
Object height H_o= all objects
Image distance = i Virtual
Image height = H_i real;inverted
Magnification : Real; inverted
```
49
Coulomb's Law
```
F= k (qq/r^2)
k= 1/4piE_o = 9 x 10^9 N m^2/C^2
```
50
Work done on a gas or by a gas
W= P Δ V
51
Electric field around a point charge
E = k (q/r^2)
52
Magnetic Field around a wire
B = (u_o I/ 2pir)
| Magnetic Flux: B A Cos θ
53
Force caused by a magnetic field on a moving charge
F= qvBsin θ
54
Entropy change at a constant T
ΔS = Q/T
55
Capacitance of Capacitor
```
C= K E_o A / d
K= dielectric constant
A= area of plates
d= distance between plates
E_o = 8.85 x 10^-12 F/m
```
56
Induced Voltage
N= # of loops
Emf = N ΔΦ / Δt
Lenz's Law - induced current flows to create a B field opposing the change in the magnetic flux
57
Transformers
```
N1/N2 = V1/V2
I1V1 = I2V2
```
58
Decibel Scale
B (decibel level of sound) = 10 log (I/I_o)
I = intensity of sound
I_o = intensity of soften audible sound
59
Poiseuille's Law
```
ΔP = 8 n L Q /(pir^4)
n = coefficient of viscosity
L= length of pipe
r = radius of pipe
Q = flow rate of fluid
```
60
Stress and Strain
```
B = stress/strain
Stress = F/A
Unit less ratios
Linear: strain= ΔL / L
Shear: strain = Δx/ L
Volume: strain= ΔV/V
```
61
Postulates of special relativity
1. Absolute, uniform motion cannot be detected.
| 2. No energy or mass transfer can occur at speeds faster than the speed of light
62
Energy of a photon
```
E = hf = mc^2
h= planck's constant = 6.64 x 10^-34 J s
f= frequency of the photon
```
63
Radioactive Decay
```
A = A_o e ^(-kt) = (1/2^n) A_o
k = (ln2)/half life
```
64
Early Quantum Physics
| Rutherford Bohr H Atoms
```
1/λ = R (1/n^2 - 1/n^2) meters^-1
R= Rydberg's constant = 1.098 x 10^7 m^-1
```
65
Mass Energy Equivalence
m_v = m_o/ Beta
Total Energy = KE + m_o c^2 = m_o c^2/ Beta
E = mc^2
66
de Broglie Matter Waves
```
E_p = h f = h c/λ= pc
Momentum : p = h / λ
For particles, p = m v = h / λ
Matter wave's wavelength must be
λ= h/ m v
```
