FRAMES OF REFERENCE

A frame of reference is a set of coordinate axes fixed to some body (or group of bodies) such as the earth, a moving train, the moon, spacecraft etc. Every measurement must be made with respect to a frame of reference. Many measurements are made with respect to the earth and it should be stated as the frame of reference. However, it is not always specified for the sake of simplicity. Everyday motion can be explained in terms of the Newtonian model.

 THE THREE LAWS IN THE NEWTONIAN MODEL: -

NEWTON’S FIRST LAW (also known as the law of inertia):

 If an object experiences no net force due to other bodies, it either remains at rest or remains in motion at the same speed in a straight line. The tendency of an object to maintain its state of motion (i.e. at rest or in uniform straight-line motion) is called its inertia. A frame of reference, in which Newton’s first law is valid, is called an inertial frame of reference. Stationary and moving (at constant speed in a straight line, i.e. at constant velocity) frames of reference are inertial frames of reference.

A non-inertial frame of reference is one in which Newton’s first law does not hold. A frame of reference that is moving with increasing or decreasing speed and/or in a curve is a non-inertial frame of reference.

NEWTON’S SECOND LAW:

The acceleration of an object is directly proportional to the net force exerted on it and is inversely proportional to its mass. The direction of the acceleration is the same as the direction of the net force.

a µ F _net -------------------- (1)

a µ 1/m --------------------- (2)

Combining the above equations we get

                                                            a µ F/m

                                                Or        a = k (F/m)

Where k is proportionality constant and in SI system the value of k is 1 so therefore putting this value in above equation we get

                                                            a = F / m

                                                Or        F = ma

In system international the unit of force is NEWTON and Newton is defined as,

            “1 kg mass accelerates 1m/sec² then total force is 1 Newton”.

NEWTON’S THIRD LAW:

 Two interacting objects, A and B, exert a force on each other, i.e. A exerts a force F_B on B and B exerts a force F_A on A. F_A and F_B are equal in magnitude but opposite in direction. Usually one is called action, the other reaction as shown in the figure.

In Newton’s third law there are always two objects and two forces involved. One force is on one object and the second force on the other. In Newton’s second law there can be one or more forces involved and they all act on the same object. Only forces that act on the same object can be added to give the net force. It is meaningless to add the two forces in Newton’s third law and say the net force is zero.

                       

                                    F_A + F_B = 0