Momentum (CIE A Level Maths: Mechanics)

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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 ( begin mathsize 16px style bold italic m end stylekg) and its velocity (begin mathsize 16px style bold italic v bold space bold m bold space bold s to the power of bold minus bold 1 end exponent end style)
    • Momentum =mv
  • The SI unit for momentum is begin mathsize 16px style bold kg bold space bold m bold space bold s to the power of bold minus bold 1 end exponent end style(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 

3-4-1-impulse

Worked example

A dog of mass  15 kg is running with speed 6 space straight m space straight s to the power of negative 1 end exponent.

Find the momentum of the dog.

3-4-1-momentum--impulse-example-solution-1

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Dan

Author: Dan

Expertise: Maths

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.