Momentum (Cambridge (CIE) AS Maths: Mechanics): Revision Note

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 ( $\mathit{m}$kg) and its velocity ($\mathit{v}\mathbf{m}{\mathbf{s}}^{\mathbf{-}\mathbf{1}}$)

  • Momentum =mv

• The SI unit for momentum is $\mathbf{kg}\mathbf{m}{\mathbf{s}}^{\mathbf{-}\mathbf{1}}$(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