Momentum and Force
Momentum= mass × velocity
p [in kgms-1 or Ns] =m [in kg]× v [in ms-1]
Momentum is always conserved assuming no external forces are acting
Newton’s second law of motion
‘The rate of change of momentum of an object is directly proportional to the resultant force which acts on the object’ so, F= mv / t
Re-arranging the equation for Newton’s second law gives :
F × t = mv ( F × t is sometimes referred to as the impulse)
Longer time the forces acts = smaller force needed for a given change in momentum
Momentum and collisions
Principle of Conservation of Energy says that:
‘Energy cannot be created or destroyed. Energy can be transferred from one form to another but the total amount of energy in a closed system will not change’
If two bodies, A and B collide and ignoring friction then:
(momentum of A)1 + (momentum of B)1 = (momentum of A)2 + (momentum of B)2
Energy in collisions
Elastic collisions = the total kinetic energy is conserved
Inelastic collisions = kinetic energy is not conserved
The missing energy has become some other form. So, Kinetic Energy = p² / 2m
V = 2 π r / T ( r= radius of circle, T= time taken for one complete revolution)
Ѳ is measured in radians Ѳ = l / r ( l= arc length, r= radius)
To covert an angle from degrees into radians ÷ the angle by 360⁰ and × by 2π
The angular velocity, ω, is given by: ω = Ѳ/ t ( units= rads-1)
Tangential velocity: v = ω r Time for one revolution: T= 2π / ω
Object moving in a circular path is always changing its direction therefore it is accelerating.
If the object is moving with constant speed, the acceleration is directed towards the centre of the circular path. This is called Centripetal acceleration, a.
a= v² / r ( r = radius, v = tangential velocity around the circle)
Since v = ω r we can re-write the expression for centripetal acceleration:
a= ω² r
The Centripetal force is the force acting on a body that is accelerating while moving in a circular path. This acts towards the centre of the circle.
F = mv² / r or F= m ω² r
Any object with charge has an electric field around it. Electric charge, Q, is measured in coulombs, C.
Coulomb’s law is used to work out the force of attraction or repulsion between two point charges.
F = KQ1Q2 / r²
Electric field strength, E, is defined as the force per unit positive charge.
E= F / Q E has units NC-1
The closer together the field lines, the stronger the field. Field lines point towards a negative charge.
Radial Field has a point charge:
Electric field strength, E=KQ / r²
Uniform Field can be produced by connecting two parallel plates to the opposite poles of a battery. The field strength is the same at all points within the field:
Electric field strength, E= V / d E has units Vm-1 ( V = potential difference)
The capacitance, C, of a system is defined as the charge stored, Q, per unit potential difference, V
C = Q / V C has units F (farads) µF = ×10-6 nF = ×10-9 pF= ×10-12
The energy stored by a capacitor is equal to the work done by the battery
W= ½ QV or W=½ CV² or W= Q² / 2C