Momentum (Cambridge International AS Mathematics)

Momentum

What is momentum?

• Any object that has mass and is moving has momentum

• Momentum measures the quantity of motion that an object has

• The momentum of a particle is defined as the product of its mass ( $m$kg) and its velocity ($vms^{-1}$)

  • Momentum =mv

• The SI unit for momentum is $\mathrm{kg}ms^{-1}$(equivalent to newton seconds N s)

• Momentum is a vector quantity - so it has a magnitude and direction

  • The direction of the momentum of a particle is the same as the direction of motion of the particle
  • The momentum is negative if the velocity is negative
  • If an object is falling vertically then momentum will be downwards

What happens when two objects are in contact?

• If two objects are in contact with each other then by Newton’s Third Law there will be equal and opposite reaction forces

• One object gains momentum from the impact and the other loses momentum

• The change in momentum will be equal for each particle provided there are no external forces

  • Remember momentum is a vector and can be negative

• For example, consider the scenario where a tennis ball is struck by a racket, suppose the momentum of the racket and the ball before the impact is 5 kg m s^-1 and -3 kg m s^-1 and the momentum of the racket afterwards is -2 kg m s^-1

  • This means the racket has a loss of 7 kg m s^-1 in momentum
  • Therefore the ball has a gain of 7 kg m s^-1 in momentum
  • Therefore the momentum of ball after the impact is 4 kg m s^-1

Worked Example A dog of mass 15 kg is running with speed $6ms^{-1}$_.

Find the momentum of the dog.

Answer: