Momentum & Impulse (Edexcel International A Level (IAL) Maths: Mechanics 1): 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 $\mathbf{kg}\mathbf{m}{\mathbf{s}}^{\mathbf{-}\mathbf{1}}$

• 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

Impulse

What is impulse?

• Impulse measures the effect of a force acting on a particle over time

• If a constant force ($\mathit{F}\mathbf{N}$ ) acts on a particle for $t$ seconds then the impulse ($\mathit{I}$) of the force is defined to be the product of the force and time

  • $\mathit{I}\mathbf{=}\mathit{F}\mathit{t}$

• The SI unit for impulse is N s(newton seconds) which is equivalent to $\mathbf{kg}\mathbf{m}{\mathbf{s}}^{\mathbf{-}\mathbf{1}}$

  • This is the same as the units for momentum

• Impulse is a vector quantity – so it has magnitude and direction

  • The direction of the impulse of a force is the same as the direction of the force

• The Impulse-Momentum Principle states that impulse is equal to the change in momentum

  • $\mathit{I}\mathbf{=}\mathit{m}\mathit{v}\mathbf{-}\mathit{m}\mathit{u}$ 

  • where m is the mass, u is the initial velocity and  v is the final velocity

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

• This means there will be equal and opposite impulses

• For example, consider hitting a tennis ball with a racket, there will be

  • an impulse exerted by the racket on the ball which propels the ball forward

  • an impulse exerted by the ball on the racket which reduces the velocity of the racket

  • The magnitudes of these impulses are equal but they are in opposite directions