# Circular motion ultra-centrifuge spin

## Homework Statement

An ultra-centrifuge has a cylindrical disk mounted on an axle that is almost frictionless. The disk spins about an axis through its centre as shown. If the disk is spinning with an angular speed of 4.50 x 10^5 rad/s and the driving force is turned off, its spinning slows down (due to air resistance) at a rate of 0.390 rad/s^2.

a) How long does the rotor spin before coming to rest?

b) during the time that it is slowing down, how many revolutions does the rotor spin before coming to rest?

c) If the disk has a diameter of 26.0 cm, find the initial linear speed of a point on the outer edge of the disk.

d) find the magnitude of the initial radial acceleration of a point on the outer edge of the disk when it first starts to slow down.

e) find the magnitude of the initial tangential acceleration of a point on the outer edge of the disk when it first starts to slow down.

## The Attempt at a Solution

a) Vf= Vi + at => t = Vf-Vi/a

is that correct? I will start off with 1st one, and will add the work i did on b-e. If someone can let me know if that is correct. If wrong please explain what i did wrong.

gneill
Mentor

## The Attempt at a Solution

a) Vf= Vi + at => t = Vf-Vi/a

is that correct? I will start off with 1st one, and will add the work i did on b-e. If someone can let me know if that is correct. If wrong please explain what i did wrong.

You will be better off working with the angular measures for this problem. The same formula can be applied to the angular measures by recognizing the analogs: d → θ ; v → ω ; a → ##\alpha##.

Other than the variables, am i on the right track?

Simon Bridge
Homework Helper
try it and see ... starting calculation without being sure you are on the right track is good practice.

you can check also your reasoning ... the situation involves constant deceleration - that sort of motion has a special name.

if you are uncertain about equations, try deriving them from a ##\small \omega## vs t graph.

gneill
Mentor
Other than the variables, am i on the right track?

You are, but it's a little early in the game to tell where the track might lead Show some more work and a result.