How Many Revolutions Does a Turbine Make When Coasting to a Stop?

[Tina20]

Homework Statement

An electric-generator turbine spins at 3460.0 rpm. Friction is so small that it takes the turbine 14.9 min to coast to a stop. How many revolutions does it make while stopping? (Do not include a unit with your answer.)

Homework Equations

rev/min * 1min/60sec = rev/sec
T (period) = 1/(rev/sec)
w (omega) = 2pi/T
wf = wi + at/r *delta t where at is tangential acceleration and r is radius

The Attempt at a Solution

346.0rev/min * 1min/60sec = 57.66 rev/sec

T = 1/57.66 = 0.0173 seconds

w = 2pi/T = 2pi/0.0173 sec = 363 rad/sec

So I did all the above, but to solve for tangential acceleration I need a radius, which is not given in the question. Once I find tangential acceleration, I can substitute it into the following equation:

Theta final = Theta initial + wi * delta t + ar/2r (delta t ^2)

and theta final can be converted into the number of revolutions.

This is a non-uniform circular motion question.

Please help :)

Tina

 

[Kurdt]

I think you can use a considerably simpler rotational equation than the one your propose.

http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html#drot