1. Newton's Laws of Motion

NEWTON'S FIRST LAW

An object will remain at rest or in uniform motion unless acted on by an external force.

This may be seen as a statement about inertia (which is an object’s tendency to resist motion, as a result of its mass). However, this is because of the second law; because a bigger mass requires a bigger force to change its motion (accelerate).

The first law is really just a special case of the second law, where the resultant force is zero.

An example of Newton's first law in action involves the centripetal force.  Without the centripetal force (which is a resultant force directed towards the centre of a circle), there will be no resultant force, and so the object will continue to travel in uniform motion. This means that it will fly off at a tangent to the point where the centripetal force ceased to exist.

NEWTON’S SECOND LAW

The rate of change of momentum of an object is directly proportional to the resultant force acting on it.
 is the mathematical way of saying the above statement.

F=ma is a special case of this law, where mass is constant:
If mass stays constant, then instead of  ,

So F=kma.

But, by definition 1 Newton is the force that gives a mass of 1 kg an acceleration of 1ms^-2 . So k=1, and hence F=ma and

So, when mass is constant,

Newton’s 2nd Law helps to define inertia: for a given resultant force, a larger mass has a smaller acceleration.

NEWTON’S THIRD LAW
If body A exerts a force on body B, then B will exert a force of the same type, same magnitude, but opposite direction, on A.

OR

For every action force there is an equal and opposite reaction force.

Sometimes this is hard to believe because the effects on one object are sometimes much greater than the other. This is due to Newton’s 2nd law – the rate of change of momentum will be the same, but for objects with a larger mass, the change in velocity will be smaller.

The forces never cancel out as they are acting on different objects.

• If a truck and a car collide, the force on the truck is just as large as the force on the car.

• A falling pebble has a gravitational force exerted on it by the Earth, and the Earth has a gravitational force exerted on it by the pebble.

• The gravitational force exerted on the Earth by the Sun is equal to the gravitational force exerted on the Sun by the Earth.

• An object resting on the floor has a force of gravity acting on it towards the Earth, and the Earth has an equal gravitational force acting on it from the object.

• When swimming, a person pushes back on the water and the water pushes back on them, causing them to move forwards. If the water didn’t push back on them, it would only cause the water to accelerate.

• A bird’s wings push down on the air and the air pushes back up onto them.

   

CONSERVATION OF MOMENTUM

In any direction, in the absence of external forces, the total momentum of a system remains constant.

From Newton’s 2nd law, the resultant force is equal to the rate of change of momentum.

From Newton’s 3rd law, each force has an equal and opposite.

The two forces in Newton’s 3rd law must exist for exactly the same amount of time, as one does not exist without the other. They must also be in exactly the opposite direction, and they are of equal magnitude.

So the force in positive direction = force in negative direction.
Change in momentum = impulse = F x t. Hence the impulses are equal in magnitude but opposite in direction, meaning they cancel out as momentum is a vector quantity, which leaves the overall change in momentum for any closed system as 0 Ns.