Newton's Laws of Motion
First Law: 
Objects have inertia, i.e. a stationary object remains stationary, or a moving object keeps on moving at the same speed in the same direction, if there is no net force acting on it 
Second Law: 
Acceleration of an object is directly proportional to and in the same direction as the net force on it, and inversely proportional to its mass. F net
= ma 
Third Law: 
When object A exerts a force on object B, B exerts a force of the same magnitude in the opposite direction on A . Fon A by B
= Fon B by A

SLM Constant Acceleration Equations
Uses: 
Equation 
v u a t 
v = u + at 
v u t s 
s = 1/2 (u + v) t 
u a t s 
s = ut + 1/2 at^{2} 
v a t s 
s = vt  1/2 at^{2} 
v u a s 
v^{2} = u^{2} + 2as 
Interpreting Motion Grpahs

d  t 
v  t 
a  t 
Direct Reading 
d at any t t at any d 
v at any t t at any v 
a at any t t at any a 
Gradient 
intsantaneous velocity at any point vavg
between any two points 
instantaneous acceleration aavg

 
Area under graph 
 
change in position 
change in velocity 
Einstein's Special Relativity
Postulate One The Principle of Relativity 
Postulate Two The Constancy of the Speed of Light 
the laws of physics are the same in all inertial frames of reference (not just mechanics) 
the speed of light is constant for all observers 
there is no 'preferred' or 'correct' frames of reference 
this implies a universal speed limit 

this has implications of simultaneity of events 
Time Dilation

γ = 1 / √*1  v^{2}/c^{2} 
t0
is proper time, t is dilated time (larger than proper time), γ is the Lorentz Factor 
Length Contraction
L = L0 /γ = L0 √1  v^{2}/c^{2} 
L 0
is proper length, L is contracted length (small than proper length), and γ is still Lorentz factor 
Magnetic Flux and Induced EMF
AC Generators (Alternators)
Transformer Equations
Across stepup and stepdown transformers 
V1 / V2 = N1 / N2 = I2 / I2

Where voltage and no. of turns are proportional to each other and current is inversely proportional. 


Centripetal Acceleration
1. Draw diagram showing all forces 
2. If required, resolve forces into components 
3. There is always a net force towards centre of circular path 
Useful equations: F net
= mv^{2} / r v = 2πr / T a = v^{2} / r = 4πr^{2} / T = 4π^{2}f^{2}r 
Energy
Conservation of Energy in an isolated system, energy is transformed from one form to another, can neither be created nor destroyed 

Hooke's Law force exerted by spring is directly proportional, but opposite in direction, to the spring's extension or compression 

Strain Potential Energy 

Gravity
Newton's Law of Universal Gravitation 
Gravitation is a force of attraction that acts between any two bodies. The gravitational force between two bodies is given by: F = GMm/r^{2} = mg 
Gravitational Fields 
Vector field, a physical quantity with value at each point in space, existing in any region with gravitational effect g = f/M = GM/r^{2} (N kg^{1}) = a(m s^{1}) 
Free Falling Objects 
influenced only by gravity net force given by: ΣF = mg a = ΣF/g = mg/g = g 
Kepler's Law 
R^{3}/T^{2} = GM/4π^{2} 
Work done 
objects moving through constant gravitational field Eg = mgΔh total energy of object moving through gravitational field is constant, even though relative amounts of kinetic and gravitational potential energy may change area under gravitational fielddistance graph gives energy change per kilo of mass 
Electricity
Electric Fields 
vector fields occurring around charged objects fields exert a noncontact force, may be attractive or repulsive 
Force on Charged Particle 
F = qE 
Coulomb's Law 
The electric force between two charges (q1, q2) is proportional to the product of the charges and inversely proportional to the square of the distance between them. 
Point Charges 
F = kq1 q2 / r^{2} where a positive value of force represents repulsion E = kQ / r^{2} (N C^{1}) 
DC Motors (Split Ring Commutators)
Changing the flux by rotating a loop


Momentum
"mass in motion" 
p = mv 
is a vector 

A net force on an object will cause a change in momentum (Impulse) 
Conservation of Momentum
If two objects collide in an isolated system, momentum will be conserved 
initial momentum = final momentum 

m1 u1
+ m2 u2
= m1 v1
+ m2 v2

OR Σ pfinal
 Σ pinitial
= Δp = 0 
Impulse
Impulse = F net
Δ t = mΔv = Δp 
is a vector 
units are either N s^{1} OR kg m s^{1} 
using this equation between two states gives us the average F net

is area under forcetime graph 
Collisions
An isolated event (no external forces and momentum is conserved) involving 2 or more objects 
Elastic Collision momentum and energy is conserved 
Usually interact (often strongly) for a short period of time 
Inelastic Collision momentum is conserved but energy is not (lost to usually heat and sound) 
Equal and opposite impulses are exerted on each other 
Work
Work(scalar) is the energy transferred to an object or transformed by the application of a force 
Work is done by a force on an object when it causes a displacement of an object in the direction of the force 
W = Fs W = Fs cosθ* 
Work done on an object: W = Fnet s 
If the energy doesn't change, or force is perpendicular to displacement, no work is done on object 
is area under forcedisplacement graph 
Magnets
Magnetic FIelds 
vector fields, denser the lines means stronger the fields field lines go from north to south pole and never touch magnets are always dipole, can never be monopole 
Earth as a Magnet 
The Earth is one large magnet – believed to be due to convection currents of molten metals in the outer core True geographic north pole is actually magnetic south pole 
Induced EMF in a Moving Conductor
Linear Particle Accelerators
Charged Particles in a Magnetic Field
Generating Voltage
We know electric currents can produce magnetic fields 
The separation of charges in the falling rod is an induced electromotive force or induced voltage (or potential difference) 
The object needs to keep moving, or the magnetic field needs to be changing for charges to remain separated (to maintain an induced voltage) 
Electromotive force (emf), is a source voltage 
Projectile Range Formula
R = u^{2}sin(20) / g 
assuming symmetric motion 
