Acceleration is the change in speed per unit of time. In a circular motion, we use the term radial acceleration. Circular motion is the type of movement of an object along with the circumference of the circle. They are uniform with a constant angular rate of rotation and constant speed or with different rates of rotation. The circular motion is divided into two components – Tangential acceleration and centripetal or radial acceleration.Â
Radial acceleration derivation
Radial acceleration is the rate of change of angular velocity whose direction is towards the center about whose circumference, the body moves. Radial acceleration is given as ‘ar’
Let the body with mass ‘m’, then the force acting on it is
F = mar …..(1)
The formula for the centripetal force acting on the stone moving in a circular motion is,
F = mv2 /r….(2)
Equating (1) and (2), we get,
mar = mv2 /r
The radial acceleration formula is then:
ar = v2/r….(3)
Formula for Radial acceleration
Equation (3) [ar = V2/r] is the formula for centripetal acceleration.
These acceleration are measured in terms of Radians per the second square, represented as ωs-2
This acceleration takes place in a uniform circular motion and the movement is concerned along the radius of an object.
A change in velocity tends to change the magnitude of radial acceleration. This implies that the centripetal acceleration is not constant, as is the case with uniform circular motion. As the speed increases, the radial acceleration also increases. If a particle moves at a higher speed, a greater radial force is needed to change the direction and vice-versa when the radius of the circular path is constant.
The circular motion adjusts its radius in response to changes in speed. Then the radius of the circular path is variable, unlike the case of uniform circular motion.
