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# Inertial Force

by Ron Kurtus (revised 11 June 2019)

When an external force is applied on an object, it will resist a change in velocity or acceleration. This resistance is called an inertial force. Since it is not an applied or external force, it is also called a fictitious force.

The concept is based on Newton's Laws of Motion, including the Law of Inertia and the Action-Reaction Law.

Inertial force can be examined both when you apply a force on an object and when a force is applied on you.

Questions you may have include:

• How does inertial force relate to Newton's Laws?
• What happens when you apply a force?
• What happens when a force is applied on you?

This lesson will answer those questions. Useful tool: Units Conversion

## Relates to Newton's Laws

Inertia is a property of matter. According to Newton's Law of Inertia, an object at rest tends to stay at rest unless acted upon by a force. Likewise, an object in motion tends to remain at that velocity unless acted upon by some force.

The concept of an inertial force comes from Newton's Laws of Motion, which can be stated as:

I. Every object in a state of uniform motion—including being stationary—tends to remain in that state of motion unless an external force is applied to it (Law of Inertia).

II. The relationship between an object's mass m, its acceleration a, and the applied or external force F is: F = ma.

III. If a force is applied to an object, there is an apparent equal and opposite reaction or resistance (Action-Reaction Law).

That equal and opposite reaction is called the inertial force. It is a factious or pseudo force equal to −F = ma.

What that means is that there is no such thing as a unidirectional force or a force that acts on only one object. There must always be two objects involved, acting on each other. One object acts on the other, while the second resists the action of the first.

## When you apply force

When you apply a force on a freely moving object in order to accelerate, decelerate, or change its direction, an equal inertial force acts on the object in an opposite direction of your applied force.

You can experience or feel that inertial force. If there were no inertial force, the object would just move when you pushed on it.

For example, when you push on an object, you can feel its resistance to the change in speed or direction.

Likewise, if you swing a ball around on a rope, you will feel the centrifugal force pulling the ball outward. That centrifugal force is an inertial force, where the ball seeks to follow a straight line.

## When force applied on you

When an applied force acts on you, you can feel the inertial force opposing the applied force. However, it is not as obvious as when a force is applied on you.

Examples include:

When you are given a shove, you feel your resistance to being moved.

When the applied force of gravity pulls you toward the ground, you can feel the opposing inertial force from your weight on the ground.

Likewise, when you are riding on a fast moving merry-go-round, you can feel the outward pull of the inertial centrifugal force on you.

Note that some sources call these forces fictitious, virtual, or pseudo forces, because there is no apparent force pushing on you. However, inertial forces do not need physical contact to oppose applied forces.

## Summary

An inertial force resists a change in velocity of an object and equal to and in the opposite direction of an applied force, as well as a resistive force.

The concept is based on Newton's Laws of Motion. Inertial force can be examined both when you apply a force on an object and when a force is applied on you.

Be active and overcome inertia

## Resources and references

Ron Kurtus' Credentials

### Websites

Force of Inertia -  Encyclopedia of Diderot & d'Alembert

Inertia - Wikipedia

Fictitious force - Wikipedia

Physics Resources

### Books

Forces In Nature by Liz Sonneborn Rosen; Publishing Group (2004) \$25.25 - Understanding gravitational, electrical and magnetic force

The Science of Forces by Steve Parker; Heinemann (2005) \$29.29 - Projects with experiments with forces and machines

Glencoe Science: Motion, Forces, and Energy, by McGraw-Hill; Glencoe/McGraw-Hill (2001) \$19.32 - Student edition (Hardcover)

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.

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