# 4.1.5 Force & Momentum

### Force & Momentum

• Force is defined as the rate of change of momentum on a body

Force is equal to the rate of change in momentum

• The change in momentum is defined as the final momentum minus the initial momentum:

pfinalpinitial

• Force and momentum are vectors so they can be either positive or negative values

Force is rate of change of momentum equation on a car hitting a wall

#### Direction of Forces

• The force that is equal to the rate of change of momentum is still the resultant force
• A force on an object will be negative if it is directed in the opposite motion to its initial velocity. This means that the force is produced by the object it has collided with

Fcar = –Fwall

• The diagram shows a car colliding with a wall
• It is the wall that produces a force of -300N on the car
• Due to Newton’s Third Law (see “Newton’s Laws of Motion”), the car also produces a force of 300N back onto the wall

#### Maths tip

• ‘Rate of change’ describes how one variable changes with respect to another. In maths, how fast something changes with time is represented as dividing by Δt (e.g. acceleration is the rate of change in velocity)
• More specifically, Δt is used for finite and quantifiable changes such as the difference in time between two events

The same change in momentum over a longer period of time will produce less force

#### Exam Tip

In an exam question, carefully consider what produces the force(s) acting. Look out for words like ‘from’ and ‘acting on’ to determine this and don’t be afraid to draw a force diagram to figure out what is going on.

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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