All You Need To Know About Momentum

In theory, every moving and colliding objects works through momentum. The momentum of an object can be calculated with the following equation:

p = mv

Where m = mass (kg) and v = velocity (m/s). To understand more about momentum, consider two imaginary spacecraft colliding and joining together.

Before the collision

Using the above equation, the momentum before the collision = mv + (-mv) which equals 0 (the mass of both objects is the same being ‘m’).

After the collision

The momentum after the two masses have collided together and more importantly ‘stuck’ together = 2m x 0 which equals 0. Therefore, momentum is conserved because the momentum before and after is the same.

Perspective of the Observer with Velocity V

From the perspective of the observer, the momentum will stay the same before and after the collision. However, this time, the observer will have a velocity of ‘v’:
• Before, p = (m x 0) + (-2mv) = -2mv
• After, p = 2m x (-v)  = -2mv

Force and Momentum

Force and momentum can be linked together in the sense that momentum = force x velocity.
Change in momentum = mass x change in velocity which is…

△p = m△v

We can assume that △p happens in time △t.

△p/△t = m x (△v/△t)

We know that △v/△t is acceleration though. Therefore…

△p/△t = ma

We know that F = ma though. Therefore…

△p/△t = Force

Force = rate of change of momentum. We can then arrange △p = F△t where ‘F△t’ is also known as the impulse force.

Rocket Science!

The fuel of mass △m is ejected in time △t and because we know that momentum is conserved, the rocket gains velocity △v.
• △p fuel = –△p rocket
• △m x (-v) = -M x △V
• △mv = M△V
However, as the rocket loses fuel, Mass, M, decreases and so △V/△t gets bigger.

Summary

• Momentum can be worked out be multiplying mass with velocity.
• The change in momentum is also know as the impulse which is Force x △t.
• Newton’s third law states that momentum is conserved.