When Sir Isaac Newton published *Philosophiae Naturalis Principia Mathematica* in 1687, he changed the world of physics forever. Newton’s work is the backbone of **classical mechanics**, useful for describing everything from the motion of planets around the sun to the motion you encounter in your day-to-day life.

In particular, Newton’s **three laws of motion** describe “everyday” motion, building upon works from those like Aristotle and Galileo to give a precise mathematical formulation of some of the most foundational laws of physics.

While quantum mechanics and Einstein’s theory of special relativity are needed to accurately describe the motion of subatomic particles or very large, or fast-moving objects, Newton’s laws of motion are still used by scientists today outside of these extreme situations.

## Newton’s First Law of Motion

The **first law**, as defined by the Physics Classroom, states that: “An object at rest stays at rest and an object in motion stays in uniform motion with the same speed and in the same direction unless acted upon by an unbalanced force.”

It’s sometimes called **the law of inertia** because it describes an object's tendency to remain unchanged (whether they’re moving or still) unless an external force is applied. Note that you need an “unbalanced” force to change an object’s velocity; two forces of equal strength pushing in opposite directions will simply cancel each other out.

This might seem strange on Earth because everything that moves eventually comes to rest, but this is only due to things like frictional force and that of air resistance. If you take your foot off the accelerator in a car, it will eventually roll to a stop because of these unbalanced forces – you’d need to keep your foot on the gas pedal to balance the forces and continue at a constant speed. If you pushed an object in space (far away from sources of gravity), it would continue moving in a straight line at the same speed until it encountered another force.

#### Tips

An object moves at a constant velocity or stays still when there is no net force applied to it.

## Newton’s Second Law of Motion

The **second law** relates net force *F _{net}* applied to an object to the product of the object’s mass

*m*and resulting acceleration

*a*. The 2nd law is stated mathematically as:

In words, **net** **force equals mass times acceleration**. So if you apply a net force of 1 newton (1 N) to an object with a 1 kg mass, you will cause it to accelerate at 1 m/s^{2} for as long as the force is applied. The law is more precisely stated as:

The bolding acknowledges that **force and acceleration are vectors** because the direction of the force and acceleration are import, as well as their magnitudes. In practice there will be multiple

*components*of each in different directions, and you need to use vector addition to fully describe the forces and motion of objects in two or three dimensions.

This explains what an “unbalanced” force is: a 5 N force in the *x* direction would be cancelled out by a 5 N force in the -*x* direction, but if the second force was in the *y* direction, they would combine into a net force and produce motion (i.e., acceleration) in a direction you can work out from the components.

## Newton’s Third Law of Motion

Newton’s **third law** is often stated as “for every action there is an equal and opposite reaction,” but a more precise formulation would be: if an object exerts a force on a second object, the second object exerts a force of equal magnitude and opposite direction on the first object.

In other words, all forces in the universe come in pairs, from the push back you feel when you try to shove a wall to the tug the Earth gives the sun in response to the gravitational tug of the sun on the Earth.

The best way to understand this is by thinking about the *normal force*. When an object rests on the ground, it is exerting a downwards force on the ground due to gravity (its *weight*), and the floor is exerting an upwards force on the object of exactly the same size, known as the normal force. Without this, the object would continue accelerating down towards the center of the Earth, which you would definitely notice the next time you tried to sit on a chair!

When you walk, your feet push down on the floor, and the floor *pushes back up against your feet* in accordance with Newton’s third law, which helps to propel you forwards.

#### References

- University of Rochester: Newton's Three Laws of Motion
- Stanford Univerity: Newton's Three Laws of Motion
- Georgia State University: HyperPhysics: Newton's Laws
- British Library: Newton's Principia Mathematica
- The Physics Classroom: Newton's First Law
- The Physics Classroom: Newton's Second Law
- The Physics Classroom: Newton's Third Law
- NASA: Newton's Laws of Motion