Question

A centrifuge rotor rotating at 9200 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.22 m?N .
If the mass of the rotor is 4.35 kg and it can be approximated as a solid cylinder of radius 0.0750 m, through how many revolutions will the rotor turn before coming to rest?
Express your answer to three significant figures.
How long will it take?
Express your answer to three significant figures and include the appropriate units.

Answer 1

Torque on the rotor will be cause by acceleration by : =/I

Here the torque and acceleration will have opposite sign that of initial angular velocity of rotor because rotor is being brought to rest.

₀  (Initial angular velocity) = 2 * rpm

Rotational inertia is of solid cylinder.

² =  ₀² + 2

Angular displacement = ² - ₀² / 2 = 0 - ₀² / 2(/I) =  -₀² / 2(/ [1/2MR² ] ) = -MR²₀² / 4

= -4.35 * 0.075 * 0.075 * ( 2 * 3.14 * 9200/60) ² / 4(-1.22)

= 4649 /2 = 740.311 rev

= 1/2 ( + ₀ ) t

t = 2 (740 /  9200 ) * 60 secs = 9.652 sec