## Maths in a minute: Newton's laws of motion

Submitted by Marianne on March 7, 2013We've been dabbling a lot in the mysterious world of quantum physics lately, so to get back down to Earth we thought we'd bring you reminder of good old classical physics.

The London Velodrome's track is designed for maximum speed using Newton's laws of motion.

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Newton's first law: An object at rest will remain at rest unless acted upon by an external and unbalanced force. An object in motion will remain in motion unless acted upon by an external and unbalanced force.*

This is also called the law of inertia and it doesn't need much explanation. No stationary object will start moving of its own accord without a force being applied. And the reason why in our everyday experience moving objects tend to slow down unless they are being powered by something is due to factors such as friction and air resistance.

*Newton's second law: The acceleration a of a body is parallel and proportional to the net force F acting on it. The exact relationship is F=ma, where m is the body's mass.*

In this equation both *F* and *a* are vectors with a direction and a magnitude.

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Newton's third law: When two bodies exert a force on each other the forces are equal in magnitude, but opposite in direction. For every action there is an equal and opposite reaction.*

Thus, if you kick a ball with your foot, then the ball exerts an equal and opposite force on your foot.

The three laws of motion were first published in 1687 in Newton's famous work *Philosophiae Naturalis Principia Mathematica* which translates as *Mathematical Principles of Natural Philosophy*. Newton's law of universal gravitation and mathematical techniques we'd now call calculus were also published in *Principia Mathematica* and together with the laws of motion they gave the first comprehensive description of the physical processes we observe in everyday life. It later turned out that the laws don't hold when you look at the world at very small scales (that's where quantum mechanics reigns) or at objects that move at very high speed or when there are very strong gravitational fields. However, Newton's laws still give a very good approximation for the physics we observe in our normal lives.