Newton's laws of motion
Various philosophers studied the basic ideas of cause of motion. According to Aristotle, a constant external force must be applied continuously to an object in order to keep it moving with uniform velocity. Later this idea was discarded and Galileo gave another idea on the basis of the experiments on an inclined plane. According to him, no force is required to keep an object moving with constant velocity. It is the presence of frictional force that tends to stop moving object, the smaller the frictional force between the object and the surface on which it is moving, the larger the distance it will travel before coming to rest. After Galileo, it was Newton who made a systematic study of motion and extended the ideas of Galileo.
Newton formulated the laws concerning the motion of the object. There are three laws of motion. A deep analysis of these laws lead us to the conclusion that these laws completely define the force. The first law gives the fundamental definition of force; the second law gives the quantitative and dimensional definition of force while the third law explains the nature of the force.
Newton's first law of motion
It states that every body continues in its state of rest or of uniform motion along a straight line unless it is compelled by an external force to change that state.
This law is based on Galileo?s law of inertia. Newton?s first law of motion deals with the basic property of matter called inertia and the definition of force.
Inertia is that property of a body by virtue of which the body is unable to change its state by itself in the absence of external force.
The inertia is of three types
1. Inertia of rest
2. Inertia of motion
3. Inertia of direction.
1.Inertia of rest
It is the inability of the body to change its state of rest by itself.
i. A person standing in a bus falls backward when the bus suddenly starts moving. This is because, the person who is initially at rest continues to be at rest even after the bus has started moving.
ii. A book lying on the table will remain at rest, until it is moved by some external agencies.
iii. When a carpet is beaten by a stick, the dust particles fall off vertically downwards once they are released and do not move along the carpet and fall off.
(ii) Inertia of motion
Inertia of motion is the inability of the body to change its state of motion by itself.
i. When a passenger gets down from a moving bus, he falls down in the direction of the motion of the bus.
ii. A passenger sitting in a moving car falls forward, when the car stops suddenly.
iii. An athlete running in a race will continue to run even after reaching the finishing point.
(iii) Inertia of direction
It is the inability of the body to change its direction of motion by itself.
When a bus moving along a straight line takes a turn to the right, the passengers are thrown towards left. This is due to inertia which makes the passengers travel along the same straight line, even though the bus has turned towards the right.
This inability of a body to change by itself its state of rest or of uniform motion along a straight line or direction, is known as inertia. The inertia of a body is directly proportional to the mass of the body.
From the first law, we infer that to change the state of rest or uniform motion, an external agency called, the force is required.
Force is defined as that which when acting on a body changes or tends to change the state of rest or of uniform motion of the body along a straight line.
A force is a push or pull upon an object, resulting the change of state of a body. Whenever there is an interaction between two objects, there is a force acting on each other. When the interaction ceases, the two objects no longer experience a force. Forces exist only as a result of an interaction.
There are two broad categories of forces between the objects, contact forces and non?contact forces resulting from action at a distance.
Contact forces are forces in which the two interacting objects are physically in contact with each other.
Tensional force, normal force, force due to air resistance, applied forces and frictional forces are examples of contact forces.
Action-at-a-distance forces (non- contact forces) are forces in which the two interacting objects are not in physical contact which each other, but are able to exert a push or pull despite the physical separation.
Gravitational force, electrical force and magnetic force are examples of non- contact forces.
Momentum of a body
It is observed experimentally that the force required to stop a moving object depends on two factors: (i) mass of the body and (ii) its velocity
A body in motion has momentum. The momentum of a body is defined as the product of its mass and velocity. If m is the mass of the body and Vector v, its velocity, the linear momentum of the body is given by Vector p = m . Vector v.
Momentum has both magnitude and direction and it is, therefore, a vector quantity. The momentum is measured in terms of kg m s -1and its dimensional formula is MLT-1.
When a force acts on a body, its velocity changes, consequently, its momentum also changes. The slowly moving bodies have smaller momentum than fast moving bodies of same mass.
If two bodies of unequal masses and velocities have same momentum, then,
Vector P1 = Vector P2
(i.e) m1. Vector v1 = m2. Vector v2
m1/m2 = Vector (v2/v1)
Hence for bodies of same momenta, their velocities are inversely proportional to their masses.