NEWTON'S LAWS OF MOTION

The British scientist and mathematician Sir Issac Newton was one of the greatest scientists of all time. A leader of scientific thought in England, he worked out how the universe was held together, discovered the secrets of light and colour and invented calculus. However, the great man had a few weaknesses. His work was often affected by his furious temper and his inability to take critisism from other scientists.


Newton's laws of motion

1st law, the law of inertia,
If the resultant force acting on a particle is zero, then the acceleration is 0.

2nd law,
The resultant force acting on a particle is proportional to the rate of change of momentum of the particle and the resultant force is in the direction of the change in momentum.
F=k.dp/dt
k=1,
F=dp/dt
=d(mv)/dt
=mdv/dt+vdm/dt
=ma+vdm/dt
If mass is constant,
F=ma.

Principal of conservation of momentum,
If the resultant force on a particle during a time period is zero then their linear momentum remains constant in that period.

Impulse,
Impulse on a particle due to a force is defined as multiplication of the force and duration of the action on the particle.

Impulse momentum theorem,
According to impulse momentum theorem impulse on a body due to a resultant force is change in its momentum.

3rd law,
If a body exerts a force on another body then the 2nd body also exerts a force on the 1st body. If any one of them is called action, the other is called reaction force. The action and reaction forces are equal in magnitude but opposite in direction. Action and reaction always act on two different bodies. They do net cancel.

Reference Frame-
It is the coordinate frame about which the position of a body with respect to some force is defined.

Inertial refence frame,
is the frame of reference that follows the law of inertia or Newton's 1st law.

Non-inertial reference frame,
is the frame of reference that doesnot follow the law of inertia.

Note,
a. A frame accelerated w.r.t. a reference frame is a non-inertial frame itself and vice-versa.
b. The earth is not perfectly an inertial frame due its rotation about its axes and revolution around the Sun.
c. In a non-inertial frame, Newton's 1st law can be applied if a special force called pseudo or false force is considered.

Pseudo force,
In an accelerating reference frame,i.e.,in a non-inertial reference frame, Newton's 1st law explains that the body in the frame experience a special acceleration and its corresponding force due to the accelerating frame and this force could be added to explain Newton's 2nd law of motion in this frame.
This special force is known as pseudo force.
Pseudo force doesnot act as action and reaction pair and thus donot follow Newton's third law as no force opposes it.