Momentum: The product of mass and velocity. p = mv.
The rate of change of momentum of a body is directly proportional to the resultant force applied to the body, and is in the same direction as the force. F = dp/dt. dp/dt is rate of change of momentum.
The product of a force applied for a certian time is known as the impulse. impulse = F x Δt = Δp
Ivestigation of rate of change of momentum
- record movement of trolly over time to calculate velocity each second, then work out momentum each second.
- Gradient of a momentum against time graph should equal the momentum because p=Ft
Conservation of linear momentum: If we calculate the momentum of each object before a collision, it should equal the total vector sum of the momentum of the objects afterwords. This depends on the condition that no external force is added.
This is directly responsible for Newtons 3rd Law
Explosions: If a stationary object 'explodes', then the total momentum of all the shrapnel parts must be zero. Zero momentum initially = Zero momentum after.
Calculating momentum in two dimensions requires resolving of vectors.
- First calculate total horizontal momentum before collision, including both objects.
- Then calculate the total momentum vertically of the two objects before the collision.
- Using Pythagoras theorem, we can work out P-total after collision. in the actual direction.
- For angle of momentum afterwards (i.e direction of velocity) use tan-1(total vertically/total horizontally).
Energy in collisions
Elastic collisions: A collision in which kinetic energy is conserved.
Inelastic collision: A collision in which kinetic energy is not conserved, such as energy being lost as heat during a collision between dodgems.
Particle collisions: Ek = 0.5mv^2 and v = p/m
These can be combined for dealing with kinetic energy of subatomic particles, although this does not take in account changes in mass due to travelling at relativistic speeds.
λ = h/p
λ = h/√2Ekm
Angular displacement is the vector measurement of the angle through which something has turned.
Angle in radians = length of arc/radius of arc
Angular velocity is ω = 2π/ T when a object completes a full circle or ω = θ/t T is the time period
and ω = 2πf as f = 1/T
For any object moving in a circle, there must be a force to cause this acceleration towards the centre of the circle - and this is called centripetal force.
F = mv^2/r is formula for centripetal force
You can easiely find centripetal acceleration when F = ma = mv^2/r therefore
a = rw^2