Balanced and unbalanced forces
When several forces act on an object, what matters is the net (resultant) force.
Balanced forces cancel out, so the net force is zero. The object's state of motion does not change: it stays at rest, or keeps moving with the same velocity.
Unbalanced forces give a non-zero net force. This changes the object's speed, direction, or both.
A box resting on the floor has its weight balanced by the push of the floor. Push it hard enough to overcome friction, and the forces become unbalanced, so the box starts moving.
Newton's first law and inertia
An object remains at rest, or in uniform motion in a straight line, unless an unbalanced external force acts on it.
The natural tendency of an object to resist any change in its state of rest or motion is called inertia. The more mass an object has, the greater its inertia. That is why a loaded truck is harder to start and to stop than a bicycle.
Everyday examples of inertia:
When a bus starts suddenly, passengers fall backwards. Their bodies tend to stay at rest while the bus moves forward.
When a bus brakes suddenly, passengers lurch forwards. Their bodies tend to keep moving.
Beating a carpet with a stick removes dust: the carpet moves, but the dust tends to stay at rest and falls out.
Seat belts stop us from being thrown forward in a sudden stop.
Momentum
The momentum p of an object is the product of its mass and velocity:
p = m v
Its SI unit is kg m/s, and its direction is the same as the direction of the velocity. A slow, heavy truck and a fast bullet can both have large momentum.
Newton's second law
The rate of change of momentum of an object is proportional to the unbalanced force applied, and takes place in the direction of the force.
For a constant mass, this becomes the familiar formula
F = m a
The SI unit of force is the newton (N). 1 N is the force that gives a mass of 1 kg an acceleration of 1 m/s².
Example. What force is needed to give a 1500 kg car an acceleration of 2 m/s²?
F = 1500 × 2 = 3000 N.
The second law also explains why a cricketer pulls the hands back while catching a fast ball. Increasing the time over which the ball stops reduces the rate of change of momentum, and so reduces the force on the hands. High jumpers land on soft mats for the same reason.
Newton's third law
To every action, there is an equal and opposite reaction.
Forces always come in pairs. The two forces act on two different objects, so they never cancel each other.
When you walk, your foot pushes the ground backwards, and the ground pushes you forwards.
When a gun is fired, the bullet is pushed forward and the gun recoils backwards.
A rocket pushes hot gases out downwards, and the gases push the rocket upwards.
A swimmer pushes water backwards to move forwards.
Conservation of momentum
When no external force acts, the total momentum of a system of objects stays constant.
In a collision or explosion, the momentum one object gains is equal to the momentum the other loses.
Example. A 4 kg gun fires a 0.02 kg bullet at 400 m/s. Find the recoil velocity of the gun.
Before firing, the total momentum is 0. After firing, 0.02 × 400 + 4 × v = 0, so v = −8 ÷ 4 = −2 m/s. The gun moves backwards at 2 m/s.