# The Three Newton’s Laws of Motion, Formula & Examples

Sir Isaac Newton is the founder of Newton’s law of motion which explains the relationship between physical objects and the forces that act upon them. This is what provides the basis of modern physics.

Sir Isaac Newton, was an astronomer, physicist, and English mathematician. He gave three laws which are proved to be fundamental when explaining the motion of a body. He developed the theories of gravitation when he was 23 years old in 1666. In 1686, he introduced the three laws of motion in the “Principia Mathematica Philosophiae Naturalis.”

With the development of these laws, science is revolutionized. Kepler’s laws together with Newton’s laws explained why planets move in elliptical orbits rather than in circles. Learn about Motion here!

Now, let’s go deep to explain the three Newton’s law of motion, their formula, and examples!

Contents

## What are the Three Newton’s Laws of Motion?

First Law – An object continues to be under a state of uniform motion unless an external force acts on it.

Second Law – The acceleration of an object depends on the mass of the object and the amount of force applied.

Third Law – Whenever one object exerts a force on another object, the second object exerts an equal and opposite on the first.

## Newton’s First Law of Motion (Law of Inertia)

The newton’s first law of motion states that “A body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force will act on it”. This is a law of inertia, i.e. suppose a block is kept on the floor, this box will remain at rest. This box will change in position only if some external force is applied to it. The first law of Newton is known as the law of inertia.

The Newton’s first law is called the Law of Inertia because Newton highlighted the inhernet property of objects and introduce the foundation of how forces can cause changes in motion. The law state that “An object continues to be under a state of uniform motion unless an external force acts on it.”

The object will continue in that state whether on rest or in uniform motion unless a net external force acts upon it.

The key takeaway on the Newton’s First Law of motion expose that an object will maintain a constant velocity in the absence of a net force resulting from unbalance forces acting upon the object. However, If the object is already in motion, it will continue to move at the same spped and direction. Also, if the object is at rest, it will remain stationary.

So, Introducing an additional external force will cause the object’s velocity to change as it respond to the applied force.

### Examples of Newton’s First Law of Motion

Below are the examples of Newton’s First Law of Motion:

1. A book will remain at rest on a table until someone or something moves it.
2. A train moving at a constant speed will continue moving in a straight line unless brakes are applied or it hits an obstacle.
3. A hockey puck glides across the ice and will keep moving in a straight line until friction or another player stops it.
4. A ball thrown in space will continue moving in the same direction indefinitely unless acted upon by an external force like gravity or collision.
5. A pendulum will stay at rest until someone pushes it, and it will continue to swing back and forth until friction slows it down.
6. A parked car will remain stationary until a force, like someone pushing or driving it, causes it to move.
7. When you stop pedaling, a bicycle continues to move forward due to inertia, eventually slowing down because of friction and air resistance.
8. An apple will remain hanging on a tree until a force, such as gravity or a gust of wind, causes it to fall.
9. An airplane flying at a steady altitude and speed will continue its motion unless forces like wind or turbulence act on it.
10. A soccer ball at rest on the ground will not move until a player kicks it.

## Newton’s Second Law of Motion (Law of Force)

The Newton’s second law of motion help us to understand how bodies respond to external forces. It describes the relationship between the force acting on a body and the resulting acceleration.

Newton’s second law state that the acceleration of an object depends on the mass of the object and the amount of force applied. This law help us to determine how much an object will accelerate when introduce to a specific net force.

Its Equation highlights the relationship between force, mass, and acceleration, creating a quantitative framework for analysing the dynamics of objects in motion.

### Formula

F=ma

Where:

𝐹
F is the net force acting on an object (measured in newtons, N).
𝑚
m is the mass of the object (measured in kilograms, kg).
𝑎
a is the acceleration of the object (measured in meters per second squared, m/s²).
This formula shows that the acceleration of an object is directly proportional to the net force applied and inversely proportional to its mass. If you apply a greater force to an object, it will accelerate more, and if the object has a greater mass, it will accelerate less for the same amount of force.

Mathematically, Newton’s Second Law can be express as:

F, represents the Force, m is the mass of the object and a is the acceleration. This is to say that the acceleration of an object is directly proportional to the magnitude of the net force introduced in the same direction as the force which is inversely proportional to the object’s mass.

Letter K is used in the second law equation to represent a proportionality constant when using the SI unit system which is Equal to 1.

Finally the Newton’s Second Law is the fundamental principle that governs the relationship between force and acceleration in physics. This law explains how external forces impact the motion of objects based on their mass and acceleration they experience.

### Problem solved on Newton’s second law of motion

Suppose a body of mass 10kg is having an acceleration of 5m/s2. What is the net force experienced by it?

Solution:

From the second law of motion, we know,

F = ma

Putting the values, we get:

F = (10 x 5) N

F = 50N

Therefore, the body is experiencing a net force of 50N.

### Examples of Newton’s Second Law of Motion

Below are the examples of Newton’s Second Law of Motion:

1. When you push an empty shopping cart, it accelerates quickly. If the cart is full of groceries, the same force will result in less acceleration.
2. When pulling a heavy box across the floor, you need to apply a greater force to achieve the same acceleration as you would for a lighter box.
3. A car accelerates faster when you press the gas pedal harder because more force is applied to overcome the car’s mass.
4. A baseball will accelerate more than a bowling ball when thrown with the same amount of force because the baseball has less mass.
5. The harder you pedal a bicycle, the faster it accelerates. The bicycle’s acceleration is proportional to the force you apply to the pedals.
6. Lifting a heavier dumbbell requires more force and results in slower acceleration compared to lifting a lighter one.
7. A rocket’s acceleration increases as more fuel is burned and more force is produced, overcoming the rocket’s mass and gravity.
8. Pushing a stalled car requires a lot of force to get it moving, and the more massive the car, the slower it accelerates.
9. When a baseball is thrown at high speed, it requires a greater force to catch and stop it, reflecting its high acceleration.
10. A light tap on a soccer ball results in slow movement, but a strong kick accelerates the ball quickly across the field.

## Third Newton’s Law of Motion (Law of Action & Reaction)

Newton’s Third Law of Motion explains the relationship between forces exerted by interacting bodies. The law states that for every action, there is an equal and opposite reaction.

This means that when two bodies interact, they apply forces on each other that are equal in magnitude and opposite in direction. In other word, the third law of motion highlights the concept that forces always occur in pairs.

Newton’s Third Law of Motion has profound implications on conserving momnetum. A moving object has certain level of momentum that can be determined by an objects of mass and velocity.  This Third Law also revealed that the total momentum of an isolated system remains constant. This means that the total momentum before and after the interaction remains the same, regardless of the forces applied.

### Examples of Newton’s Third  Law of Motion

Below are the examples of Newton’s Third Law of Motion:

1. As the rocket expels gas downwards, an equal and opposite force pushes the rocket upwards.
2. When you walk, your foot pushes backward on the ground, and the ground pushes your foot forward with an equal force, allowing you to move.
3. When you push water backward with your hands while swimming, the water pushes you forward, propelling you through the water.
4. If you jump off a small boat onto the dock, the boat moves backward as you move forward, due to the equal and opposite forces.
5. A bird pushes air down with its wings, and the air pushes the bird up, allowing it to stay in flight.
6. When a gun is fired, the bullet moves forward, and the gun moves backward with equal force, resulting in recoil.
7. When you push against a wall, the wall pushes back with equal force, which is why you don’t move through it.
8. When you row a boat, the oars push water backward, and the water pushes the boat forward.
9. In a tug-of-war, when one team pulls on the rope, the other team pulls back with equal force. The teams remain stationary if the forces are equal.
10. When you throw a ball against a wall, the wall exerts an equal and opposite force, causing the ball to bounce back towards you.

Learn how force changes the state of motion here!

That is all for this article, where I explained the three Newton’s law of motion, their formula, and examples. I hope it was helpful, if so, kindly share with others. Thanks for reading, see you around!