Can a rotor ever come to a complete stop with a negative angular acceleration?

[Kevinc]

I just got done taking a test and on of the problems read: A rotor is turning at 200 rpm and has an angular acceleration of -0.015w rads/s^2. How many seconds before the rotor is at 200rpm. How many revolutions before the rotor comes to rest.

Here is my method for solving:
w initial = 200rpm = 20.9 rads/s

a = dw/dt = -0.015w rads/s^2
dw/w = -0.015dt
ln(w) = -0.015t
integrating both sides yeilds
w = Ce^-0.015t
w = 20.9e^-0.015t

I got the correct answer for the first part, but seeing that this is exponential decay I answered that the rotor would never come to a complete rest. I was told that I have the wrong answer. My teacher demonstrated the "correct" approach.

a = (dw/dtheta) x (dtheta/dt) = (dw/dtheta)w = -0.015w
(dw/dtheta) = -0.015
dw = -0.015 dtheta
using 20.9 - 0 and 0-theta for limits of integration yields
-20.9 = -0.015theta
theta = 1393 rads or 222 revolutions


My assumption seems more logical that the rotor would never stop spinning under those circumstances and would there for have infinite revolutions, but i am unable to find any holes in my teachers method.
If anyone can point out any errors in either mine or my teachers method or give any explanation why to seemingly correct methods would yield different answers I would really appreciate it.

 

[tiny-tim]

Welcome to PF!

Hi Kevinc! Welcome to PF!

(have an omega: ω and a theta: θ and try using the X² tag just above the Reply box )

My assumption seems more logical that the rotor would never stop spinning under those circumstances and would there for have infinite revolutions …

Even if it does never stop spinning,

why would that mean there would be infinite revolutions? ​

 

[Kevinc]

Yea your right that was a dumb assumption. It could possibly converge on a specific angle as t goes to infinite. So does it converge on 222 revs as t goes to infinite?

 

[tiny-tim]

I haven't checked your figures, but I assume so.

 

[Kevinc]

I just integrated my angular velocity equation to get the angle equation and turns out as t goes to infinite theta goes to 222 revs. I put in my answer that the rotor never comes to rest so technically i am correct and it never actually reaches 222 revs so technically he is incorrect. I think I now have a good argument for the teacher. Thanks for the help.