Formulas Flashcards
Power
Rate of work done
Power= Work/time Unit: Watt
Efficiency of Work
Work_out/Energy_in
Heating a solid, liquid, or gas formula
Q= m c ΔT c= specific heat Q= heat added
Linear Momentum
p=mv
Momentum is conserved in collisions
Centre of Mass
Point masses on a line
x_cm= Sum of (mx)/M_total
Pressure under Water
P= p g h p = density of water h= dept of water
Universal Gravitation
F= G (mm/r^2) G= 6.67 x 10^-11 N m^2/kg^2
Mechanical energy
PE_grav= P = mgh KE_linear= K = 1/2mv^2
Snell’s Law
n1sinθ=n2sin θ
Index of refraction
n=c/v
c= speed of light 3 x 10^8 m/s
Periodic Waves
v= f λ f= 1/T T = period of wave
Bouyant Force
Fb= p V g = (m_displaced fluid)g = weight_displaced fluid p= density of the fluid V= Volume of the fluid
Ohm’s Law
V= IR V= Voltage I= current R= resistance
Resistance of a Wire
R= p L / A_x p= resistivity of wire material L= length of the wire A_x= cross sectional area
Heat of a phase change
Q= m L L= latent heat of phase change
Hooke’s Law
F= k x
PE of spring
W= 1/2kx^2 = work done on spring
Electric Power
P = I^2R = V^2/R= IV
Speed of wave on string
T = mv^2/L T = tension in string m = mass of string L = length of string
Projectile Motion
Horizontal: x-x_o = v_o t + 0
Vertical: y-y_o = v+o t + 1/2at^2
Centripetal Force
F= mv^2/r = mw^2r
Kirchhoff’s Law
Loop Rule: Sum_around any loop Δ V_i=0
Node rule: Sym_at any node I_i=0
Minimum speed at the top of a Vertical circular loop
v=Sqrt(rg)
Resistor Combos
Series: R_eq= R1+R2+R3….
Parallel = 1/R_eq
Newton’s second law and Rotation Inertia
τ = torque = I α I = moment of inertia = m r^2
Circular unbanked tracks
mv^2/r = umg
Continuity of fluid flow
A_in v_in = A_out v_out
A = Area
v= velocity
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
Capacitors
Q= CV Q= charge on capacitor C= Capacitance V= voltage applied
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)
Ohm
Volt/amp
Farad
Coulomb/ Volt
Thermal Expansion
Linear: ΔL = L_o alpha ΔT
Volume: ΔV = V_o beta ΔT
Bernoulli’s Equation
P + p g h+ 1/2 pv^2= constant
Q_Volume Flow Rate= A1v1 = A2v2= constant
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
Angular Momentum = L
L= I w= m v r sin θ
Angular impulse equals change in Angular momentum
ΔL= torque Δt= Δ(I w)
Period of Simple Harmonic Motion
T = 2 pi sqrt(m/k) k = spring constant f = 1/T = 1/period
Banked Circular tracks
v^2 = r g tan θ
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
Flower of Heat through a Solid
ΔQ/Δt = (k A ΔT)/ L k = thermal conductivity A = area of solid L = thickness of solid
PE stored in Capacitor
P = 1/2 C V^2
RC Circuit Formula (Charging)
V_e = V_cell (1-e^(-t/RC))
RC = time constant
V_cell- V_capacitor - IR = 0
Simple Pendulum
T = 2pi sqrt (L/g) f = 1/T
Sinusoidal motion
x= A cos (wt) = A cos (2pi f t) w= angular frequency f= frequency
Doppler Effect
f' = f (343 (+_) v_o)/(343 (_+) v_s) v_o= velocity of observer v_s= velocity of source
2nd Law of Thermodynamics
Change in internal energy of system is ΔU = Q added + W done on - Q lost - W done by
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
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
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
Coulomb’s Law
F= k (qq/r^2) k= 1/4piE_o = 9 x 10^9 N m^2/C^2
Work done on a gas or by a gas
W= P Δ V
Electric field around a point charge
E = k (q/r^2)
Magnetic Field around a wire
B = (u_o I/ 2pir)
Magnetic Flux: B A Cos θ
Force caused by a magnetic field on a moving charge
F= qvBsin θ
Entropy change at a constant T
ΔS = Q/T
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
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
Transformers
N1/N2 = V1/V2 I1V1 = I2V2
Decibel Scale
B (decibel level of sound) = 10 log (I/I_o)
I = intensity of sound
I_o = intensity of soften audible sound
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
Stress and Strain
B = stress/strain Stress = F/A Unit less ratios Linear: strain= ΔL / L Shear: strain = Δx/ L Volume: strain= ΔV/V
Postulates of special relativity
- Absolute, uniform motion cannot be detected.
2. No energy or mass transfer can occur at speeds faster than the speed of light
Energy of a photon
E = hf = mc^2 h= planck's constant = 6.64 x 10^-34 J s f= frequency of the photon
Radioactive Decay
A = A_o e ^(-kt) = (1/2^n) A_o k = (ln2)/half life
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
Mass Energy Equivalence
m_v = m_o/ Beta
Total Energy = KE + m_o c^2 = m_o c^2/ Beta
E = mc^2
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
