We have assumed in a uniform circular motion that the particle’s speed is constant as it goes around the circle. If the speed varies, we call the motion non-uniform circular motion. In non-uniform circular motion, Eq 1.19 still gives the radial component of acceleration which is always perpendicular to the instantaneous velocity and directed toward the center of the circle. But since the speed v has different values at different points in the motion, the magnitude of the centripetal acceleration is not constant. The radial (centripetal) acceleration is greatest at the point in the circle where the speed is greatest. In non-uniform circular motion there is also a component of acceleration that is parallel to the instantaneous velocity. This component of the acceleration that arises due to change in magnitude of the velocity is tangent to the circle and it is known as tangential acceleration (a_t).

Key terms

• Uniform circular motion: motion along a circle at a constant speed.
• Centripetal acceleration: acceleration that arises due to change in direction of tangential velocity.
• Tangential acceleration: acceleration that arise due to change in magnitude of tangential velocity.