## Newtons Laws Of Motion

Isaac Newton

Isaac Newton was a physicist, astronomer and mathematician. Newton is remembered for his work in mechanics, optics, astronomy, mathematics and his famous description of gravity. Mechanics is the study of things that are moving. Newton’s mechanics offered the first explanation of Kepler’s laws (Kepler didn’t say why the planets move the way they do, he described their movement mathematically).

Newtonian (or Classical) mechanics is the first topic studied by a student physicist. It provides us with our first introduction to mathematics (particularly calculus) as a practical tool, and remains a useful description of nature throughout our careers.

There are many equations used when analysing the interaction of moving bodies, but with a little ingenuity they can all be derived from Newton’s three laws of motion.

# Newton’s Laws of Motion

## Newton’s First Law

Every body will remain in a state of rest or constant velocity unless acted on by a force

When a physicist talks about a body, he/she means a lump of matter that can be taken as one object. Footballs and bullets are bodies. Two bodies stuck together with Blu-Tack count as a single body. A body at rest is sitting still and not doing anything interesting. A body with a constant velocity is moving at a constant speed in a straight line.

This means:

• A football sits still unless you kick it (duh!).
• After a football has been kicked it ‘wants’ to travels in a straight line at a constant speed, but it doesn’t because air resistance slows it down and the earths gravity pulls the trajectory into an ellipse.

## Newton’s Second Law

The rate of change of velocity is directly proportional to the force applied and occurs in the same direction.

This is expressed as:

$F=ma$

The terms in this equation are:

$F$ = The force applied.

$m$ = The mass of the body.

$a$ = The acceleration (rate of change of velocity) of the body.

Since the acceleration is equal to the rate of change of velocity we can also write this equation as:

$F=\frac{d}{dt}(mv)$

This equation tells us that the harder you push the harder a body accelerates.

## Newton’s Third Law

For every action there is a reaction, that is both equal and opposite.

This law is often misunderstood, but is really very simple. When something applies a force, it itself experiences the same force (that causes an acceleration in the opposite direction).

This can be experimentally tested by punching a brick wall. Your fist applies a force on the wall. The wall applies the same size force to your fist (in the opposite direction). This is why it huts if you punch the wall.