*Elena Cox*

# Laws of Inertia: Definition & Formula

## Definition

Place a book on your desk. Does the book move? Unless you move the book, it will remain where you put it without moving.

Imagine a spacecraft moving through space. When the engines are turned off, the spacecraft will coast through space at the same speed and in the same direction.

The book and the spacecraft have **inertia**. Inertia is the property of an object that resists changes in its motion. Because of inertia, an object at rest tends to stay at rest. An object in motion tends to keep moving at a constant speed in a straight line.

## Newton's First Law

**Newton's First Law of Motion** explains how inertia affects moving and non-moving objects. Newton's first law states that an object will remain at rest or move at a constant speed in a straight line unless it is acted on by an unbalanced force. **Inertia** comes from mass. Objects with more mass have more inertia.

To understand inertia, imagine moving a bowling ball and a golf ball that are at rest. The golf ball has a mass of 0.05 kilogram, and the bowling ball has a mass of five kilograms. The bowling ball has 100 times more mass than the golf ball, so it has 100 times more inertia, too.

Now ask yourself, which needs more force to start moving? If you push for the same distance, the bowling ball takes much more force to get it moving the same speed as the golf ball. The bowling ball needs more force because a bowling ball has more inertia than a golf ball. The greater an object's inertia, the greater the force needed to change its motion.

According to Newton's first law, an unbalanced force is needed to move the book on your desk. You could supply the force by pushing the book.

An unbalanced force is needed to change the speed or direction of the spacecraft. This force could be supplied by the spacecraft's engines.

Because of inertia, an object at rest will remain at rest until something causes it to move. Likewise, a moving object continues to move at the same speed and in the same direction unless something acts on it to change its speed or direction.

## Effects of Inertia

You can feel the effects of inertia every day. Suppose you are riding in a car. What happens if the car comes to a sudden stop? Your body has inertia. When the car stops, you keep on moving forward. What happens when the car starts moving? Because of inertia, your body tends to stay at rest when the car moves forward.

In baseball, inertia tends to keep a player running in a straight line. So, base runners have to 'round' the bases instead of making sharp turns.

An **oscillator** is a physical system that has repeating cycles (harmonic motion). A child on a swing is an oscillator, as is a vibrating guitar string. A wagon rolling down a hill is not an oscillator. Systems that oscillate move back and forth around a center, or **equilibrium**, position. You can think of equilibrium as the system at rest, undisturbed, with zero net force. A wagon rolling down a hill is not in equilibrium because the force of gravity that causes it to accelerate is not balanced by another force. A child sitting motionless on a swing is in equilibrium because the force of gravity is balanced by the tension in the ropes.

A **restoring force** is any force that always acts to pull a system back toward equilibrium. Restoring force is related to the force of gravity or weight and the lift force (or tension) of the string of a pendulum. If a pendulum is pulled forward or backward, gravity creates a restoring force that pulls it toward equilibrium. Systems with restoring forces become oscillators.

Inertia causes an oscillator to go past equilibrium. The motion of an oscillator is the result of an interaction between a restoring force and inertia. For example, the restoring force pulls a pendulum toward equilibrium. But, because of Newton's first law, the pendulum does not just stop at equilibrium. According to the first law, an object in motion tends to stay in motion. The pendulum has inertia that keeps it moving forward so it overshoots its equilibrium position every time.

## Examples

Cars and planes with more inertia take more force to **accelerate**. Since inertia is related to mass, in order to reduce inertia you must reduce mass. The mass of a car or plane is a trade-off between inertia and the strength of materials of the car or plane. You want strong materials, but you don't want them so heavy that it takes too much energy (fuel) just to get the car or plane moving!

Seat belts could be called 'anti-inertia' belts. A car tends to keep moving in a straight line, even if the driver's foot is not on the gas pedal. Everyone inside the car also has inertia. They are moving at the same speed as the car.

Suppose you are riding in a car. The driver is forced to step on brakes suddenly. Inertia keeps you moving forward at the same speed as the car was moving. You will keep moving until something stops you. This might be the car's steering wheel, dashboard or windshield. You might be hurt if you hit these parts of the car, unless you are wearing a seat belt. A seat belt keeps you from moving forward when the car stops suddenly. Seat belts can prevent serious injuries. You should always remember to 'buckle up' when you get into a car.

If you suddenly apply the brakes to your rapidly moving bicycle, you have to brace yourself to keep from falling forward. If you are on a ride at an amusement park in which you suddenly accelerate forward, your body seems to push back against the seat.

In both cases you have demonstrated Newton's first law, the **Law of Inertia**. The Principle or Law of Inertia states: a mass at rest tends to remain at rest; a mass moving at a constant velocity tends to keep moving at that velocity, unless acted upon by an outside force. Thus, Newton's first law involves the problem of changing velocity, or of acceleration. For instance, suppose you are standing still in a 'bumper car' at the amusement park and someone drives another car into yours.

You will be accelerated from zero kilometers per hour to some value greater than zero. The force of collision is able to move your car. This unbalanced force produces acceleration. Newton's First Law of Motion states that no force is needed to keep something moving in a straight line at a constant speed. A force is needed to stop that motion or to change it in some way. This is a description of inertia, which is a property of all things.

You are probably used to thinking that moving objects eventually slow down by themselves. But this slowing down is the result of forces such as friction. Without such forces, an object set moving would move forever.

The car and the red block in this pair of images can serve as another example of the Law of Inertia.

In the left panel, both objects are moving to the right. In the right panel, the wooden box applies a force to the car, causing it to stop. The red block does not experience the force applied by the wooden box. It continues to move to the right with the same velocity as in the left panel.

Is inertia a force? No. **Forces** are results of interactions between two objects; they are not properties of single objects, so inertia cannot be a force. Remember that because velocity includes both the speed and direction of motion, a net force is required to change either the speed or the direction of motion. If the net force is zero, Newton's first law means the object will continue with the same speed and direction.

**Mass** is a measure of inertia because an object with a large mass is harder to start in motion and harder to stop than an object with a smaller mass. This is because the object with the large mass has greater inertia. For example, imagine that you are going to push a grocery cart that has only one potato in it. No problem, right? But suppose the grocery cart is filled with potatoes. Now the total mass - and the inertia - of the cart full of potatoes is much greater. It will be harder to get the cart moving and harder to stop it once it is moving.

## Lesson Summary

**Inertia** is the tendency of an object to remain at rest or in motion. **Newton's First Law of Motion** states that an object will remain at rest or move at a constant speed in a straight line unless it is acted on by an unbalanced force. The effects of inertia can be felt every day.

## Noteworthy Terms

**Newton's First Law of Motion**: explains how inertia affects moving and nonmoving objects; the first law states that an object will remain at rest or move at a constant speed in a straight line unless it is acted on by an unbalanced force**Oscillator**: a physical system that has repeating cycles (harmonic motion)**Equilibrium**: the system at rest, undisturbed, with zero net force**Restoring force**: any force that always acts to pull a system back toward equilibrium**Accelerate**: a change in velocity**Law of Inertia**: a mass at rest tends to remain at rest; a mass moving at a constant velocity tends to keep moving at that velocity unless acted upon by an outside force

## Learning Outcomes

Once you have reviewed the lesson at length, you could realize these goals:

- Recognize the meaning of the term 'inertia'
- State Newton's First Law of Motion
- Understand the effects of inertia
- Discuss several examples of the laws of inertia

To unlock this lesson you must be a Study.com Member.

Create your account

### Register to view this lesson

### Unlock Your Education

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.

Become a MemberAlready a member? Log In

Back