Question

A speck of dust on a spinning DVD has a centripetal acceleration of 15 m/s2 .

What is the acceleration of a different speck of dust that is twice as far from the center of the disk?

What would be the acceleration of the first speck of dust if the disk's angular velocity was doubled?

Please express your answer to two significant figures and include the appropriate units.

Answer 1

1.

Centripetal acceleration is given by:

ac = w^2*R

w = angular velocity

R = radius of circular rotating object

Given that point is twice as far from the center of the disk, and DVD is spinning at the same rate, So

centripetal acceleration is directly proportional to the distance of point from the center

So,

ac_2/ac_1 = R2/R1

ac_2 = ac_1*(R2/R1)

Since R2/R1 = 2, So

ac_2 = 2*15

ac_2 = 30 m/sec^2

Part B.

ow given that at the same point angular velocity is doubled, Since centripetal acceleration is directly proportioanl to the square of angular velocity, So

ac_2/ac_1 = (w2/w1)^2

ac_2 = ac_1*(w2/w1)^2

Since w2/w1 = 2, So

ac_2 = 15*2^2

ac_2 = 60 m/sec^2

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