# Momentum

Momentum is the product of mass and velocity -

p = mv

Momentum has two parts to it. The velocity 'v' of the object and also the mass 'm' of the object.

Change in momentum is Δmv - often written mΔv, as it is usually just the velocity that changes (but sometimes mass does too)

Δp = mΔv

You can apply an impulse to change the momentum of an object.

Impulse = Ft = Δp

Impulse has two factors to it - the force applied and the time over which it acts.

The force applied is equal to the rate of change of momentum of the body.

F = Δp/t

F = mΔv/t

so, F=ma

### Momentum is a vector

Velocity is a vector so momentum is a vector. Velocity is speed in a particular direction.

Momentum has direction associated with it too.

If two bodies were moving in opposite directions their momentum would have opposite signs, just as their velocities would have opposite signs. This becomes very important when two or more bodies hit each other.

### Application of momentum to everyday situations

 If you are used to catching balls you know that catching a fast light ball can hurt your hands as much as catching a slow heavy one. It can make your hands sting... this is because your hand has to supply the force to change the momentum of the ball to zero (a stopped ball has a momentum of zero as its velocity will be zero and momentum is the product of mass and velocity). Your sports coach will have taught you to extend the time you spend making the ball stop. By increasing 't' the 'F' is smaller and your hand stings less. So by reaching out for the ball and then pulling it towards you as you catch it you risk hurting yourself less than if you stop it 'dead'. You need the same impulse to bring the ball to a standstill - you just choose to have a longer 't' and smaller 'F' and that makes the catching experience more comfortable. You need to think about that force in terms of pressure too. If you wear a glove to catch a ball the contact area with that ball is greater when you catch it. You therefore experience less pressure from the force when you stop it. This makes damage to your hand less likely - as it is pressure from a force that causes the potential damage.

 One of the main applications of this knowledge (that examiners love to ask questions on!) relates to car safety - see 'crumple zones', 'air bags' and 'seat belts'. Make sure you can explain how they work in terms of manipulation of the time and force factor of the impulse that causes momentum change.