One dimensional motion
Scalar and vectors(fram)
Scalar - measure(quantity)
Vector - scalar with direction
Frame of reference - point of view for measure
Displacement
Displacement - change in position
△x = x(final) - x(start)
*△ - changing/delta
*can be a vector
*sign(+/-) of displacement possible to interpret like a direction, and then △x is vector
*displacement is a distance but not a travelled distance(path)
**in classical mechanics time(t) is sort of displacement
Speed and velocity
*velocity is a vector
V(vel)=S(displacement)/t(time) | in km/h, m/h, km/s, etc
*speed is a scalar
V(speed)=S(distance)/t(time)
**it is average velocity, or possible to calc a constant velocity
**also possible to calc average velocity through sum:
(v(f)+v(i))/2
Instantaneous speed
speed can changes while moving through a path or going through displacement
*in different positions in time possible to calc V(inst) = △s/△t = (x(2)-x(1)) / (t(2)-t(1))
*tangent in s/t graphic(slope)
*area under graph is the distance
Acceleration
Measure of changing the speed through time
a = △ V / △ t (m/(s^2))
*a = (V(final) - V(initial)) / △ t
Kinematic formulas
*for constant acceleration
Formulas:
v(f)=v(i)+a*△t
△x=((v(i)+v(f))/2)*△t
△x = v(i)*t + ½*a*△t^2 | △x = v(f)*△t - ½*a*t^2
v(f)^2 = v(i)^2+2*a*△x
Variables : v(i), v(f), a, t, △x
*g ~=9.81 m/s^2; standard gravity acceleration(on surface of the earth)
Two dimensional motion
cos(angle) = Viy / Vi
sin(angle) = Vix / V
*break Vi(two dimensional motion) to two one dimensional(Vix, Viy)
i
Vf = -Vi
Total displacement
S = sqrt(Sx^2 +Sy^2)
*total velocity with the same logic(pythagoras theorem)
Forces and Newton’s Laws of motion
Net force(ΣF) - sum of all forces to an object
*force quantity measure is N(Newtons)
First law
Bodies still rest when forces is balanced, or keep going straightly(inertia)
*when ΣF = 0 then a = 0, V - const
Second law
F = m*a (N, kg*m/s^2)
*m - mass, quantity of inertia
Third law
When applying the force - getting the equal opposite force
F(A->B) = -F(B->A)
*normal force(Fn)
F - Fn = 0
Weight
Force of mass to the ground(gravity force)
F = m * g = W
Inclined surface
*because F=mg parallel to vertical(cross angles)
Force of friction
Prevents moving of objects on surface
Static friction
coefficient of static friction μ(s) = Fs/Fn
*Fs horizontal application
*when start to moving after budge
*after F(push/pull)>Fs - start to slide
Kinetic friction
coefficient of kinetic friction μ(k) = Fk/Fn=
*Fk vertical application of force
*when sliding
*in cases of wheel, kinetic is only when sliding but not when moving but in start it is static
Thermodynamics
When reducing volume:
(P1*V1)/T1 = (P2*V2)/T2
*T - in kelvins
** 0 k = -273 Celsius
PV = nRT
*n - quantity in moles
*R - molar gas constant
**n*N(a) = quantity of molecules
**N(a) - Avogadro number
***PV = N*k(b)*T
***N - numbers of molecules
***k(b) - Boltzmann's constant
Heat
Transfer:
Q = mcΔT (heat, transfer energy to defined temperature)
*c- specific heat
Q1+Q2+Q3=0 (when interact)
Fusion/vaporizing:
Q = mL (energy for change state by fusion,vaporizing)
*L - latent heat of fusion/vaporization
* Q(total) = Q(for heat) + Q(for change)
Thermal conduction rate:
Q/t=k*A*(T2-T1)/d
*k - thermal conductivity constant
*A - area
First law of thermodynamics
Energy can not be destroyed only converted
Internal energy
ΔU=Q(+/-)W
U=(3/2)*P*V
work as isotermic(without an adding additional temperature):
W=nrt*ln(Vf/Vi)
ΔU=W
W=PΔV(area under curve)
Second law of thermodynamics
ΔS(universe) >= 0
Entropy
ΔS = Q/T
heat added to the system to temperature which was applied
Efficiency
nu = W/Q
heat given to work executed
nu = 1 - Q2/Q1
nu = 1 - T2/T1
Electrodynamics
Coulumb's law:
F = (k*q1*q2)/r^2
*k Culons coeffient
conservation law: Sum of charges is constant
**also F is U - potential energy between when moving charge.
Electric field cause electric force
E(vector) = F(electrical, vector) / Q2
*Q2 charge in the E field
E = (k*Q1)/ r^2 - field created by Q=]\
Ohm's Law
V= I*R
*I = Δq/Δt - through area
*V = ΔU/q
power = ΔU/Δt
Magnetism
Force = q*v*B*sin(a)
B - magnetic field in tesls
v - speed of moving a charge
q - the charge
*on wire F = B*I*L*sin(a)
*magnetic field by wire B = mu*i/2pir, where mu - permeability of space
EMF(ElectroMotiveForce for wire) = L*V*B*sina
*V - velocity of moving wire(charge) through B magnetic field
Magnetic flux: B*A*cos(a) how much magnetic field is going through area
Voltage generated by flux: V=-N*flux/t
*also EMF for wire loop in magnetic field
*N how many loops
Transformer ratio: V1/V2= N1/N2
Light
Light is electromagnetic wave while radiating
speed of light c = lambda*v
*lamda wavelength, v - frequency
*c is constant
When absorbing,emiting, delta of energy:
E = h*v
*h - Planck's constant
Young's double slit problem
d*sin = m *lambda
*d - distance between slit
*m - order of light pattern
**same for multiple slit with same distances(same pattern)
**for single slit w*sin = m *lambda, w-width, lambda between destructive moments
In thin film d = 2t, t deep of the film
*interference only when from fast to slow layer
Va/lambda(a)=Vb/lambda(b)
Optics
Shell's Law
Refraction:
*v=c/n , where n - is refraction index of material
sin(a)/sin(b) = v(a)/v(b) = n
Linses:
1/d(object) + 1/d(image) = 1/f
h(object)/h(image) = d(object)/d(image) = f/d(object)
n2>n1 => f2>f1
Mirror equations:
h(object)/d(object)=h(image)/d(image)
1/d(object) + 1/d(image) = 1/f
*also working for lenses
**f for concave = -f
d(object)/d(image) = h(object)/h(image)
Power of lense = 1/f (diopters)
Relativity
Lorentz transformation
γ = sqrt(1 - v^2/c^2)
β = v / c
x' = γ(x - βct)
x' = γ(x - vt)
x = γ(x' + vt')
t' = γ(t - vx/c^2)
Einstein velocity addition
μ = Δx/Δt
Δx'/Δt' = (μ - v)/(1 - μv/c^2)
Quantum
Photoelectricity
E = h* Nu
*Nu - frequency
h*Nu = A+(mv^2)/2
p = (h*Nu)/c = h/alpha
*alpha - wave length
alpha = c / f = h / p
Electron
2pir= n * alpha
r(n) = n^2*(r1)
KE = ½ * (k e^2)/r
PE = (k e^2)/r
En = E1/(n^2)
Absorption/Emmision:
hc/lambda = E(1)-E(2)
1/lambda = r(1/(n1^2) - 1/(n2^2))
Half-life
N(t)=No*e^(-labda*t)
t^(½)=.693/lambda
