Newton's Laws

Newton’s First Law

A body will maintain a constant velocity (including rest), unless an external force is applied to that body.

Newton’s Second Law

The resultant force on a body is equivalent to its mass, multiplied by its acceleration. Remember, the acceleration will be in the same direction as the resultant force. To be exact, we have the equation

$F = ma$

So, just as an example, in the Resolving Forces section, we’ve referenced the equation $W = mg$, relating weight to mass and the force of gravity. Weight is a force, and the value of $g$ is given as $9.8text{ ms}^{-2}$, which is an acceleration.

Newton’s Third Law

When two bodies collide, they exert forces upon each other which are equal in magnitude but opposite in direction.

You might have heard the phrase, “every action has an equal and opposite reaction”. So, let’s say you lean against a wall. Since you are exerting a force on the wall, the wall exerts an equal force back on you.

Newton’s Laws in Vector Form

We can also apply $F = ma$ to a system with multiple components, by applying the formula to each component separately.

Example: say a $4text{ kg}$ particle is travelling with an acceleration $underline{a} = 2textbf{i} + 3textbf{j}$.

Then its force $F$ is given by $F = 4(2textbf{i} + 3textbf{j}) = 8textbf{i} + 12textbf{j}$.