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In uniform circular motion, an object is said to move tangentially along a circular path with a changing tangential velocity but a constant tangential speed. The velocity changes because the direction of it is constantly changing at every point of its journey. This is said to be due to the "centripetal acceleration" which is directed inward towards the center of the circle. There is a formula for the centripetal acceleration which gives a value and a direction. And correct me if I am wrong, this centripetal acceleration is considered not constant because its direction is also changing. My question is this, if there is a value for centripetal acceleration. Shouldn't there ought to be a value termed "centripetal velocity" because if acceleration towards the center exists, shouldn't there be velocity towards the center as well? I don't see this term anywhere really so wanted to hear your thoughts.

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Shouldn't there ought to be a value termed "centripetal velocity" ?

The usual term for this is "radial velocity" - the component of the velocity vector that is parallel to the radius vector. You can split any vector into two components relative to a fixed central point - one is the radial component, which is parallel to the radius vector, and the other is the tangential component, which is perpendicular to the radius vector. So a velocity vector can be split into a radial component and a tangential component.

If acceleration towards the center exists, shouldn't there be velocity towards the center as well ?

No, not if the motion is circular. In circular motion the radial velocity is always zero (because the radius is constant throughout the motion) so the only component of velocity is the tangential velocity component. Since the velocity vector is perpendicular to the radius vector, it is also perpendicular to the centripetal force (which is parallel to the radius vector). A force that is perpendicular to the velocity vector changes the direction of the velocity vector but does not change its magnitude. And in uniform circular motion the centripetal force is exactly the right size to keep the velocity vector perpendicular to the radius. Hence the velocity vector changes direction but has a constant magnitude, and is always tangential to the circle.

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  • $\begingroup$ I appreciate your explanation of this, using radial velocity component and relating it to the radius really helped me see this better. $\endgroup$
    – thuang
    Apr 9, 2023 at 16:44

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