OCR B: Chapter 11 & 12

The momentum of a object: momentum = mv

It is always conserved, so for example the total momentum of 2 objects before a collision is equal to the total momentum after: m1u1+m2u2 = m1v1+m2v2

Newtons laws

• The velocity of an object will not change unless acted on by a external force
• Force is the rate of change of momentum (F =ma) or F = Δp/Δt
• Every action has a equal and oppose reaction

Work done = Fs

Energy cannot be created or destroyed, in can only be transferred from one form to another. The energy of a closed system will stay the same.

KE = 1/2mv^2   GPE = mgh   EPE = 1/2kx^2

Impulse = change in momentum

The angular speed is radians per second ( ω = θ/t). Angual and linear speed are linked by the equation v = rω

The frequency in circular motion is the number of complete revoltuions per second. The period is the time taken for a complete revolution. The equation which relates these two is : f = 1/T.  In terms of angular speed: ω = 2πf or ω = 2π/T

Objects travelling in a circle are accelerating even if they are going at a constant speed, since the direction and therefore velocity is changing. This is called the centripedal acceleration and is produced by the centripedal force which acts towards the cente of the circle.

a = v^2 / r    and F = mv^2 / r

If this centripedal force did not exist, the object would follow a tangent.

An object will experience a force when put in a gravitational field. The force is always attractive: F=-GmM / r^2

You can draw gravitational field lines around a mass. Since gravity is attractive, the direction is always towards to centre of the mass.

The field strength is the force per unit mass. It can be worked out using g = F/m or the equation g=-GM/ r^2. In can also be called the acceleration due to gravity. 

The force in a uniform gravitational field can be calculated using F=mg

Gravitational potential energy is equal to mgh in a uniform field or E = -GMm /r in a non uniform field. It is the work which would need to be done to move a mass against the force of gravity. Potential energy is zero at infinity and negative on the earths surface.

The gravitational potential is the potential energy per unit mass V = E /m or V=-GM/r. Equipotentials in a diagram shows all the points in a field which have the same potential. No work is done moving across them.

• Measure using radar. A short pulse of a radio wave is sent towards a distant object, they are reflected of the object. You can use the time it takes to reflect and the speed of light to find the distance. 2d =ct. You can also use this to find out the average speed of the object by sending out two pulses. The assumptions are that the time taken to get to the object is the same time taken to return and the speed of the radio waves is the same on the way and the way back.
• Calculate using brightness. Brightness = luminocity / r^2. This works with cepheid variables as you can calulate the brightness directly.
• Distances can be measured in AU, light years and other forms of measurment.

You can measure the speed of objects using the doppler effect.

If something is moving away from you, the frequency will decrease. If it is moving towards you the frequency will increase. The greater the speed, the more the change.

^{λm -} λo / λo = v/c  if v << c    v is positive in redshift, v is negative in blueshift

You can work out the shift using absorption spectra to work out the change in wavelength.

Hubble's law is that recessional velocity of galaxies is proportional to distance: v = H0.d .This is evidence that the universe is expanding.  It is seen that the galaxies arent actually moving through space, instead space its self is expanding, as well as the waves within it. This is called the cosmological red shift

The hot big bang theory says that the universe started off very hot and dense, and has been expanding ever since. There are several pieces of evidence for this:

• Hubbles law
• The cosmic microwave background radiation. The expansion of the universe causes the electromagnetic radiation produced in the very early universe's wavelength to increase, and it is therefore now detected in the microwave region. 
• The amount of helium in the universe. The early universe was hot enough for hydrogen fusion to happen.

A estimate of the age of the universe = 1/H0. It is an estimate since the universe probably hasnt expanded at the same rate all the time.

1. All planets orbit the sun with an elliptical, not a circular one

2. As they orbit they cover equal areas in equal time

3. T^2 α R^3

Where v is the moving object and 0 is the stationary object,

mv = m0.γ

tv=t0.γ

lv = l0 / γ

1st assumption: The laws of phyics work in all inertial refrence frames

2nd assumption: The speed of light is the same in all inertial reference frames

In a space-time diagram, light will always travel at 45 degrees