How are centripetal acceleration and radius related? If you double the radius, t

Question

How are centripetal acceleration and radius related? If you double the radius, the centripetal acceleration will?

Ok, so ac = v2/r. Mathmatically it is evident to see that centripetal acceleration and radius are inversely proportional to each other.

But, since the velocity here is only the linear part of the velocity, and the angular velocity is constant, centripetal acceleration will decrease as radius increases and is inversely proportional.

So which velocity do I assume is kept constant in this question? I will get different relationships between radius and centripetal acceleration!

Explanation / Answer

centripetal force,

Fc=m*v^2/r

m*a=m*v^2/r

==>

centipetl acceleration, a_c=v^2/r

here,

magnitude of the a_c decreases as increases the radius of the circler path

and

velocity, v=r*w

now,

a_C=(r*w)^2*r

a_c=w^2*r

here,

direction of the centipetal acceleration is inward and along the radius vector

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