Question

How the centripetal force depends on the radius a) if the frequency is constant, b) If the speed is constant. You must document your answer with formulas.

(Please write clearly )

Answer 1

Centripetal force is given by:

Fc = M*V^2/R

V = w*R

V = linear speed

w = angular speed

R = radius

M = mass

Fc = M*V^2/R = M*(w*R)^2/R = M*w^2*R

we know that angular velocity is given by:

w = 2*pi*f

Fc = M*4*pi^2*f^2*R

So if frequency is constant, then centripetal force is directly proportional to the radius.

Fc2/Fc1 = R2/R1

Part B

Fc = M*V^2/R

So if speed (V) is constant, then centripetal force is inversely proportional to the radius.

Fc2/Fc1 = R1/R2

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