(This revision material will be meaningful and useful only when you have read HC Verma's Chaper)
First law of motion
If the (vector) sum of all the forces acting on a particle is zero then and only then the particle remains unaccelerated (i.e., remains at rest or moves with constant velocity).
We can say in vector notation
a = 0 if and only if resultant force F = 0
A frame of reference in which Newton's first law is valid is called an inertial frame of reference.
A frame of reference in whch Newton's first law is not valid is called a noninertial frame of reference. (Example: lamp in an elevator cabin whose cable had broken)
Example of lamp in an elevator who cable had broken:
In the cabin when on measures with reference to the cabin, the lamp hanging from the ceiling has no acceleration. Hence the forces acting on the lamp, its weight (W) and the tension in the string supporting it are balancing each other W = T.
But for an observer on the ground, lamp is accelerating with acceleration g, when he considers the forces acting on the lamp as w and T once again, W is not equal to T as lamp is accelarating. Both cannot be right at the same time, and it means in once of the frames Newton's first law is not applicable.
All frames moving uniformly with respect to an inertial frame are themselves inertial.
Examples: A train moving with uniform velocity with respect to ground, a plane flying with uniform velocity with respect to a high etc. The sum of forces acting on a suit case kept on the shelves of them with turnout to be zero.
Second law of motion
The acceleration of a particle as measured from an inertial frame is given by the (vector) sum of all the forces acting on the particle divided by its mass.
a = F/m or F = ma
Acceleration and force are measured at the same instant. If force becomes zero at an instant, acceleation also becomes zero at the same instant.
Third law of motion