Newton's Laws of Motion
Sir Isaac Newton (1642-1727) formulated three fundamental laws of motion that are still useful today for analysing the behaviour of objects.
The physical laws formulated by Newton are often described as "classical physics" or "Newtonian" physics. These laws were not superseded until Albert Einstein's Theory of Relativity. However for small speeds and weak gravity (both applicable on Earth), Newton's laws are accurate enough for "everyday" purposes.
Newton's First Law
An object that is moving at a particular speed in a particular direction will stay moving at that particular speed and in that particular direction unless it is forced to change.
In other words, objects will not change their velocity unless they have a force acting on them. This includes objects at rest. An object at rest will not start moving unless it has a force acting on it.
This law is often a source of confusion when describing motion. For example, a person not wearing a seatbelt is often described as being "thrown" from a car in an accident. What is really happening is that the person kept moving because there was no force to make them stop. No force actually "threw" them from the car.
Another car example is the feeling of "being pushed back in your seat" when a car accelerates. In reality, the force on you is the seat pushing against you to force you to change speed at the same rate as the car and go in the car's direction.
Newton's Second Law
The acceleration an object experiences is directly proportional to the force.
In other words, if an object is experiencing a force, the acceleration will be directly proportional to the force. This is where the equation \( F = ma \) (\( F \) is force, \( m \) is mass, \( a \) is acceleration) comes from.This law is the "classical physics" description of mass: mass is the ratio between force and acceleration.
Newton's Third Law
Every action force has an equal and opposite reaction force.
Newton's third law means that all forces are mutual. To exert a force, you must have something to "push against".
There are many everyday examples of this:
- Earth's gravity: We are attracted to the earth by gravity. But, by Newton's Third Law, the earth is also attracted to us by gravity with an equal force. Even in free fall, the earth is accelerating towards us.
- Helicopter tail rotors: The engine in a helicopter generates torque to spin the main blades. The tail rotor is required to provide the reaction force for the main rotor torque so that the helicopter itself doesn't spin.
- Forces between current-carrying wires: Current carrying wires are repelled (or attracted) to each other with equal force on both wires.
Newton's Third Law even explains why a space ship can propel itself in a vacuum. A space ship that burns fuel propels itself by pushing the exhaust backwards. In turn, the force of making the exhaust go backwards exerts a force on the space ship that makes the space ship go forwards.
A full treatment of Newton's Third Law requires understanding of the concept of momentum, but a detailed discussion of this is beyond the scope of this course.
It is important not to confuse force with acceleration and movement! In the free-fall example, the object will accelerate towards the earth at 9.81 ms-2. While the attractive forces between the Earth and the object are the same according to Newton's Third Law, the accelerations will be vastly different.As an example, a 10 kg cannonball will be attracted to Earth with a force of 98.1 N. It's acceleration is \( \frac{98.1}{10} \) = 9.81 ms-2.
By Newton's Third Law, the earth is also attracted to the cannonball with a force of 98.1 N. But the Earth has a mass of 5.972 · 1024 kg. Therefore the Earth's acceleration towards the cannonball is equal to \( \frac{98.1}{5.972 \cdot 10^{24} } \), or 1.64 · 10-23 ms-2. The cannonball will be doing by far the majority of the movement in this example. It is easy to see why many people think that the Earth doesn't move when something falls towards it. However, while the movement is extremely small, it is not zero.