Question

A speck of dust on a spinning dvd has a centripetal accelera- tion of 20 m/s2.
a. what is the acceleration of a different speck of dust that is twice as far from the center of the disk?
b. what would be the acceleration of the first speck of dust if the disk's angular velocity was doubled?

Answer 1

The centripetal acceleration of an object spinning in a circle is
a = v²/r = 20 m/s²
where
r =  the distance of the object from the center of the circle
v = the tangential velocity of the object

The centripetal acceleration is also given by
a = rω² = 20 m/s²
where
ω = the angular velocity.

Part a.
If the radius is doubled while the angular velocity remains constant, then
the centripetal acceleration will double.
a = (2r)ω² = 2*20 = 40 m/s²

Answer: 40 m/s²

Part b.
If the angular velocity is doubled, then
a = r(2ω)² = 4rω² = 4*20 = 80 m/s²

Answer: 80 m/s²