Acentrifuge rotor rotating at 9700 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.96 m⋅n . part a if the mass of the rotor is 4.00 kg and it can be approximated as a solid cylinder of radius 0.0350 m , through how many revolutions will the rotor turn before coming to rest?

We start from the definition of Torque,

Where ,

I = moment of inertia

Angular acceleration.

The torque given in the problem is 1.96mN.

We look for the moment of inertia of a solid cylinder,

Where m is the mass of 4Kg and R the radius 0.035m

Replacing,

A) With angular acceleration we can find the number of revolutions, the given equation would be,

B) We apply the rotational dynamics formula and we can find the time,

= initial pressure

= final pressure = 2

= initial volume

= final volume = /4

= initial temperature = 20 c = 20 + 273 = 293 k

= final temperature = ?

using the equation