⦿ Chapter : Circular Motion ⦿ Topic : Prove that the centripetal acceleration of a body revolving in a circular orbit of radius r is ac = v^2/r
Acceleration is defined as the rate of change of velocity. Now since acceleration and velocity both are vector quantities, they depend on direction. So, either change in the magnitude of the velocity and direction of the velocity. In a circular motion, there is always an acceleration because the velocity of the object is continuously changing.
Centripetal acceleration is the rate of change of tangential velocity, and centripetal force is the force acting that helps generate an object’s centripetal acceleration in a circular motion. The centripetal force is directed towards the centre and therefore is perpendicular to the motion of the body. The force applied to a body moving in a uniform circular motion is known as centripetal acceleration. In a circular motion, the centripetal force would be perpendicular to the velocity.
A centripetal force is a force that makes a body follow a curved path. The direction of the centripetal force is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". In the theory of Newtonian mechanics, gravity provides the centripetal force causing astronomical orbits.
One common example involving centripetal force is the case in which a body moves with uniform speed along a circular path. The centripetal force is directed at right angles to the motion and also along the radius towards the centre of the circular path.