Our current ideas of motion and rest were developed by Galileo Galilei and Sir Isaac Newton in the seventeenth century. These ideas developed by Galileo and Newton are included in ‘Classical Physics’ or ‘Newtonian Physics’.
Newton had a very huge contribution in classical Physics including his ‘Laws of Motion’ and his ‘Universal Law of Gravitation’. Classical Physics is more complete in itself.
On the other hand, ‘Modern Physics’ includes two major theories — ‘Einstein’s Theory of Relativity’ (containing Special Relativity and General Relativity) and ‘Theory of Quantum Physics’ (including quantum mechanics and the quantum field theory). The general theory of relativity and quantum field theory are quite incomplete or partial theories.
The Meaning of Motion, Rest and Force
Motion, rest and force are the basic concepts of Mechanics (and Physics). It is very important to know the basic definitions of motion, rest and force before proceeding onto Newton’s Laws.
‘Motion’ is something which is always around us. An object is said to be in motion if it changes its position. But, this definition is incomplete. We can understand this with an example.
Suppose there are two trains, ‘A’ and ‘B’, moving in the same direction with equal ‘speeds’, and, a person standing stationary on the platform. Now, what we can say about the motion of the train ‘A’? Is it changing its position? For a person sitting in train ‘B’, train ‘A’ is not moving because both the trains are moving at the same speed. But, for the person standing on the platform, the train ‘A’ is in motion as it is changing its position with respect to him.
So, from the above example, we can conclude — An object is said to be in motion if it changes its position with respect to any other object or with respect to ‘Time’. But, what is time now? A clear definition of time can’t be given. In classical Physics, we can understand time as an ‘interval’ between two events. According to Relativity, time is a ‘dimension’.
It can be concluded that motion is always relative. But, now, how can we measure this motion? For measuring motion, we generally use two physical quantities, ‘Speed’ and ‘Velocity’.
Speed is the rate of change of ‘distance’. In simple words, speed is the measure of the change in distance (position, more precisely) with time. Mathematically,
Speed = Distance / Time
As we measure distance in ‘metres’ (m) and time in ‘seconds’ (s), the unit in which speed is measured is ‘metres per second’ or ‘m/s’..
Velocity is nothing but ‘speed with direction’. The unit of both speed and velocity are also the same, that is, m/s. If we define the direction of speed, it is known as velocity. For example, if we say a man is running with 10 m/s, it is his speed, but, if we say the man is running with 10 m/s in the north direction, it is his velocity.
Another difference in both quantities is that, as direction changes with time, the velocity changes, but the speed may or may not change. For example, 10 m/s in the north and 10 m/s in the south are two different values of velocities, but equal speeds.
If we talk about ‘Rest’, it is nothing but a special case of motion, with ‘velocity equals zero’.
Another quantity for measuring motion is ‘Acceleration’. It is actually a measure of the change in velocity with respect to time. Mathematically,
Acceleration = (Final Velocity − Initial Velocity) / (Time)
If velocity remains constant, acceleration will be equal to zero as there will be no ‘change’ in velocity.
‘Force’ is a push or pull which changes or tends to change the position of an object. It is a very big misconception in Physics that an object can only be set in motion by a force. But, motion is already there. A force always changes the state of motion of an object, but it may or may not cause motion. It actually depends on the state of the observer. We should take an example to make this concept more clear.
For example, suppose a person standing stationary in space and no force is acting on it. An observer, moving with some velocity, passes by it. Now, with respect to that observer, the object is in motion, but no force acted on it.
Now, suppose, the observer is at rest and the object or person which is being observed is also at rest (with respect to the observer). Now, a force acts on that person. Now, it is set in motion. But, in this case also, the force actually changed the state of motion from zero velocity to some definite velocity.
So, actually, motion is already there. A force can only change the state of motion. Motion simply refers to the change in position of an object with respect to any other object or observer.
In a nutshell, a force is always responsible for the change in state of motion. But, it may or mayn’t “cause” motion. All this is dependent upon the reference frame (observer) we take.
Newton’s Laws of Motion
Sir Isaac Newton provided three ‘Laws of Motion’ in which the second law is one of the most fundamental laws of Physics.
To, understand Newton’s Laws, we should first discuss a property called ‘Inertia’.
Inertia and Galileo’s Experiment
Galileo discovered a property that every object with a mass possesses called ‘Inertia’. He did a simple experiment (illustrated in Fig 1.3), which is as follows:
- He placed two slopes opposite to each other.
- The slopes were friction-less (friction is a force which opposes the motion of an object on a surface).
- He placed the ball on one slope and the ball came down because of gravitation (or gravity).
- Now, the ball went up on the second slope and it reached the same height from which it was left (or, say dropped).
- Then he decreased the angle of the second slope and repeated this experiment, the result was the same, the ball reached the same height from which it was dropped.
- Then he reduced the angle of the second slope to zero. Now, the ball didn’t stop and continued to move in order to achieve its original height.
He concluded from this observation that every object resists the change in its state of motion and this property of an object is called Inertia. Greater the mass of a body, the greater its inertia.
Galileo’s experiment is illustrated below.
A daily life example of inertia is the jerk felt by a person standing inside a bus when the bus suddenly stops moving. Actually, the legs of the person are connected directly to the floor of the bus. As the bus suddenly comes into rest, the legs of the person stops, and, as the upper part (which is not connected directly to the bus) was in motion, so it will resist the change in state of its motion and would like to remain in motion, and the person will feel a ‘pseudo-force’ in forward direction due to inertia.
This example is illustrated in below.
Newton’s First Law – The Law of Inertia
On the basis of Galileo’s calculations, Newton formulated his first law of motion (also referred to as the law of inertia).
This law states that a body will continue its state of motion or rest until a force acts on it.
You might have seen some examples of this law in your daily life. When you make a ball roll on the ground and leave it, it continues its state of motion and doesn’t stop. It stops only after taking some time because of the frictional force applied by the floor.
Newton’s Second Law – The Law of Action
Physically, a force can be defined as a push or pull which changes or tends to change the position or state of an object.
Newton’s Second Law of Motion provides a mathematical definition of force. It states that the force applied on an object is equal to the rate of change of momentum.
‘Momentum’ is simply the product of an object’s mass and its velocity. If we define momentum ‘physically’, momentum is the physical quantity which tells us that how much force an object will apply on another object (or experience a force by another object) when both the objects will collide with each other.
In simple words, it can also be defined as ‘combined effect or impact of mass and velocity’. It can be understood by an example.
Suppose light is coming towards you from an electric bulb. Light’s speed (or velocity) is the speed limit of the universe (according to special relativity) and light is very ‘fast’. It can cover a distance if 300,000 kilometres in only a single second.
Light is composed of very small particles called ‘Photons’. Now, when the light will reach you, that is, when photons will collide with you, will you feel any force? The answer is certainly no. This is because photons have almost zero mass, so their momentum will also become almost zero and ultimately the force will also be negligible.
But now suppose a car of about 100 kilograms moving at a speed near (but smaller) to the light, and it collides with another car at rest or moving towards the first car. The results will not be very good in this case.
This is because both the mass and velocity are very large, so momentum will be larger than both the quantities and force will also be huge.
Now, we should come on the term, ‘Rate of change of momentum’. It is the change in momentum with respect to time.
It is nothing but the difference in the final momentum (momentum after the application of force) and the initial momentum (momentum before the application of force) and dividing this difference by the time in which the momentum has changed.This gives us the value of the rate of change of momentum, and, the rate of change of momentum is equal to the force, according to the second law of motion.
As described above, momentum is the mass of an object multiplied by its speed (or velocity). So, initial momentum will be the mass multiplied by initial velocity and final momentum will be mass multiplied by final velocity. So, mathematically, the rate of change of momentum is equal to:
[(Mass × Final Velocity) − (Mass × Initial Velocity)] / [Time]
As mass is multiplied by both final and initial velocity, we can take mass common, and write the above expression as:
Mass × (Final Velocity − Initial Velocity) / (Time)
Now, we know that change in velocity (i.e. Final Velocity − Initial Velocity) divided by time is nothing but acceleration, so we can write:
Rate of Change of Momentum = Mass × Acceleration
Newton’s second law of motion states that the rate of change of momentum is force, so:
Force = Mass × Acceleration
So, the force applied on an object is simply equal to the mass of the object multiplied by the acceleration produced in it (due to the application of force on it). This is a very fundamental law of Physics. This above equation also concludes that a force always produces an acceleration.
We can also prove the first law of motion using the second law.
If the force applied on an object is zero (that is, no force is working on it), this means that whether the mass is zero or acceleration is zero. And, a force can be applied on an object which has some mass, so, mass can’t be zero.
So, acceleration will be zero, which means that the velocity hasn’t changed, so, the object will continue its state of rest (velocity equals to zero), or uniform motion (that is, velocity will remain constant without any acceleration) if force is not applied on the object.
Newton’s Third Law – The Law of Reaction
The third law of motion states that a force applied to an object has an opposite and equal reaction. In simple words, “To every action, there is an equal and opposite reaction”.
The action and reaction forces always act on two different objects. For example, when you walk you push the ground backwards (but it doesn’t move due to having a very large mass), and, in turn, the ground pushes you forward.
So, the action and reaction act on two different bodies and the directions of both are opposite. So it can be concluded that,
(Action Force) = − (Reaction Force)
(Reaction Force) = − (Action Force)
There is a negative sign in the above equations to represent the opposite direction.
Newton’s Theory of Gravity
Newton is best known for his ‘Law of Universal Gravitation’. This concept of gravity, started by Newton, unified the terrestrial with celestial as Newton said that the reason for an apple falling on Earth and the Moon orbiting the Earth is the same. This reason was ‘Gravitation’ or simply ‘Gravity’.
Newton’s theory of gravity states that every single object in the universe attracts every other object in the universe with a force which varies directly to the product of the masses of the two objects and this force varies inversely to the square of the distance between them.
This means that larger the masses of the two objects (or single one), the larger the force of gravity and larger the distance between the two objects, the smaller the force. For example, if the mass of any single body is doubled, the force between the two bodies will be doubled and if the distance between them is doubled, the force between them will reduce to one-fourth of the original force.
The value of the force of gravity in Newton’s theory is given by the equation below:
In the equation, ‘F‘ is the force of gravity between two objects of masses ‘M‘ and ‘m’ separated by a distance of ‘R‘.