## Centripetal force in circular motion

Centripetal force in circular motion: 1. According to Newton’s law of motion, whenever a body moves in a straight line with uniform velocity, no force is required to maintain this velocity. But when a body moves along a circular path with uniform speed, its direction changes continuously i.e., velocity keeps on changing on account of a change in direction. According to Newton’s second low of motion, a change in the direction of motion of the body can be place only if some external force acts on the body.

2. Due to inertia, at every point of the circular path; the body tends to move along the tangent in the circular path at the point shows in following figure. Since everybody has directional inertia, a velocity cannot change by itself and as such we have to apply a force. But this force should be such that it changes the direction of velocity and not its magnitude. This is possible only if the force acts perpendicular to the direction of the velocity. Because the velocity is along the tangent, this force must be along the radius (because the radius of a circle at any point is perpendicular to the tangent at the point). Further, as this force is to move the body in a circular path, it must act towards the centre. This center-seeking force is called the centripetal force. Hence, centripetal force is that force which is required to move a body in a circular path with uniform speed. The force acts on the body along the radius and towards the center.

3. Thus we find that a body in uniform circular motion is in a continuous accelerated motion and the acceleration is directed along the radius of the circular path and towards the center. It is called centripetal acceleration. It has been proved earlier that for a body moving with an uniform speed v in a circular path of radius r, it is given by:

a=v^{2}/r=ω^{2}r

Where ω represents the uniform angular speed of the body.

**Hence, centripetal force required to move a body of mass M along a circular path of radius r is given by:**

F = Mv^{2}/r=M ω^{2}r