# 5.7.5 Inertia

Higher Tier Only

### Inertia

• The concept of inertia is closely related to motion, it is defined as:

The tendency of an object to continue in its state of rest, or in uniform motion unless acted upon by an external force

• In other words, inertia is an object’s resistance to a change in motion
• If an object is at rest, it will tend to remain at rest
• If an object is moving at a constant velocity (constant speed in a straight line), it will continue to do so
• The image below illustrates the concept of inertia using a coin and a cup of water:

Demonstrating the inertia of a small coin

Higher Tier Only

### Inertia & Mass

• Inertial mass is the property of an object which describes how difficult it is to change its velocity
• It is defined as the ratio between the force applied to it and the acceleration it experiences:

• Where:
• m = inertial mass in kilograms (kg)
• F = force in newtons (N)
• a = acceleration in metres per second squared (m/s2)
• This equation shows that for a given force, inertial mass is inversely proportional to acceleration
• Larger inertial masses will experience small accelerations
• Smaller inertial masses will experience large accelerations

This collection of objects have a variety of inertial masses. For the same applied force, their accelerations are inversely proportional to their mass

#### Worked Example

Three objects are used by a physics technician to demonstrate the concept of inertial mass.

She applies the same force to each of the three objects and notes that:

• Object A accelerates at 1.5 m/s2
• Object B accelerates at 0.7 m/s2
• Object C accelerates at 2.0 m/s2

Which object has the largest inertial mass?

Step 1: State the definition of inertial mass

• Inertial mass is defined as the ratio of force to acceleration

Step 2: Apply the definition to each of the objects in the question

• Because each object experiences the same force, inertial mass is inversely proportional to acceleration
• This means that the object with the largest inertial mass will experience the smallest acceleration
• Object B has the smallest acceleration, so it has the largest inertial mass

#### Exam Tip

The definition of inertial mass as a ratio between force and acceleration should look similar to Newton’s second law. That’s because when you calculate the mass of an object using Newton’s second law, you are in fact calculating its inertial mass.

### Author: Jonathan

Jonathan graduated with a first-class Master's degree in Theoretical Physics from Imperial College London. He has worked in education for more than a decade as a Maths and Physics Teacher, Tutor, Head of Physics, and most recently, as Assistant Headteacher. He is now an Educational Consultant and works with us to design and improve our Physics resources.
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