CIRCULAR MOTION

When a particle moves in a circular path with uniform speed, its motion is called uniform circular motion. This motion takes place in a plane hence to specify the

Angular Displacement:

The unit is radian.

Angular velocity

The rate of change of angular displacement is called angular velocity. Its unit is radian/s.

From the above expression, we conclude that when a rigid body undergoes rotation, angular velocity of all its particles is same but linear velocity is different since its value is proportional to R.

CENTREPETAL ACCELERATION:

When a particle undergoes uniform circular motion, its direction changes continuously but its speed remains constant. Due to continuous change in direction, its velocity changes. We know from kinematics that change in velocity gives rise to acceleration; this acceleration is known as centripetal acceleration. It is always directed to the center of motion.

This is directed to center and perpendicular to velocity.

VARIABLE CIRCULAR MOTION:

In variable circular motion, the magnitude of speed changes unlike in case of uniform circular motion. Since, magnitude of velocity also changes in this case; we have tangential acceleration a_T along with centripetal acceleration a_C .

Tangential acceleration is directed along tangent, so direction of net acceleration is given by vector rule. Since neither acceleration is a constant, hence the net acceleration is also not a constant.

CENTREPETAL FORCE:

A body in circular motion experiences an acceleration hence it is also acted upon by a force, this force is called centripetal force. Centripetal force is always directed towards center. Its magnitude is given by:

Note: centripetal force is not a new force. Any force in nature may acts as a centripetal force.

CENTRIFUGAL FORCE:

It is also referred to as pseudo force. Since this force is not actually felt by the particle. This force comes into play when observer is observing any motion from an accelerated frame.

For example: a man standing on earth looking at a table might find it rotating about a fixed axis but when the same man is standing on a rotating table will find it at rest.

Now to explain this situation, we can say that when the observer observes the motion from the frame of table, then he finds it at rest because centripetal force is then balanced by centrifugal force. So no net force on the body and it appears to be at rest. But, when the same man is observing the motion from ground frame of reference, there is no centrifugal force and only centripetal force that is responsible for its motion.

Hence, we can safely say, centrifugal force is a pseudo force that needs to be applied on any object in motion when the observer is observing the motion from the rotating/accelerating frame of reference.