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 ( $v m s^{- 1}$ )
- Momentum =mv
The SI unit for momentum is $kg m s^{- 1}$ (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

3-4-1-impulse

Worked example

A dog of mass 15 kg is running with speed $6 m s^{- 1}$ _.

Find the momentum of the dog.

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

Momentum (CIE A Level Maths: Mechanics)

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What is momentum?

What happens when two objects are in contact?

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1. Mechanics Toolkit

1.1 Quantities, Units & Modelling

1.1.1 Scalars & Vectors

1.1.2 Fundamental Units

1.1.3 Derived Units

1.1.4 Types of Force

1.1.5 Modelling Assumptions

2. Kinematics (Straight Line Motion)

2.1 Kinematics Graphs

2.1.1 Displacement-Time Graphs

2.1.2 Velocity-Time Graphs

2.1.3 Drawing Travel Graphs

2.2 Variable Acceleration

2.2.1 Using Calculus in 1D

2.3 Constant Acceleration

2.3.1 Deriving the suvat Equations

2.3.2 suvat in 1D

2.3.3 Acceleration due to Gravity

3. Forces & Newton’s Laws

3.1 Forces

3.1.1 Force Diagrams

3.1.2 Equilibrium in 1D

3.1.3 Equilibrium in 2D

3.2 Newton's Second Law

3.2.1 F = ma

3.2.2 Connected Bodies - Ropes & Tow Bars

3.2.3 Connected Bodies - The Lift Problem

3.2.4 Connected Bodies - Pulleys

3.3 Further Forces & Newton's Laws

3.3.1 Resolving Forces & Inclined Planes

3.3.2 Coefficient of Friction

3.3.3 Coefficient of Friction - F = ma

3.3.4 Coefficient of Friction - Inclined Planes

3.3.5 Coefficient of Friction - Harder Problems

4. Energy, Work & Power

4.1 Work & Energy

4.1.1 Work

4.1.2 Energy

4.1.3 Energy Principles

4.2 Power

4.2.1 Power

5. Momentum

5.1 Momentum & Collisions

5.1.1 Momentum

5.1.2 Direct Collisions

5.1.3 Collisions - Multiple Collisions

Author: Dan