A solid disc with radius R is is spinning. An object exerts a force F at the edg

Question

A solid disc with radius R is is spinning. An object exerts a force F at the edge of the disc to slow down the disc. The disc slows down to rest in 6 seconds. How long would the disc take to stop if:
a) the mass of the disc doubled 12 S
b) the radius of the disc doubled 12 S
c) the force doubled 3 S

(Treat each variable independently in parts a-c -- for example, keep the mass and force constant when doubling the radius.)
d) You exert a force F on the outer edge of a solid disc of thickness d and radius R, which results in a certain angular acceleration. If instead you were to try to angularly accelerate (with the same angular acceleration) a solid disc made of the same material and with the same thickness, but with 3 times the radius, what force would be required (in terms of the force F exerted in the first situation)?
Force required is? F

Explanation / Answer

r F = I alfa

F = 0.5 M R^2 alfa/R = 0.5 M R alfa

when we increase R to 3R, the mass M will increase to 9M

F' = 0.5 M' R' alfa = 0.5 (9M) (3R) alfa = 27 (0.5 M R alfa)

Force requared is 27 F

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