Angular Acceleration Homework: 962 Revolutions in 10 Secs

[Wes Turner]

Homework Statement

A computer disk starts from rest, then speeds up with angular acceleration of 190 rad/s^2. until it reaches its final speed of 7200 rpm. How many revolutions will it have made 10.0 secs after starting up?

Homework Equations

w = w0 + at
rps = rpm / 60
1 rev = 2*pi rad
1 rad = 1/(2*pi) rev
190 rad/s^2 = (190/(2*pi)) rev/s^2 = 30.24 rev/s^2
7200 rpm = 7200/60 rps = 120 rps

The Attempt at a Solution

Calculate the time it will take to get up to full speed.
w = w0 + at
7200 rpm = 0 rpm + 190 rad/s^2 * t
120 rps = 0 rps + 30.24 rev/s^2 x t
t = 120 rev/s / 30.24 rev/s^2 = 3.97 s

Over the first 3.97 s, it the angular velocity increases linearly, so the average is 120 rps/2 = 60 rps.
At 60 rps for 3.97 sec, it completes 238 revolutions.

That leaves 10 s - 3.97 s = 6.03 s x 120 rps = 724 revolutions.

Then 238 + 723 = 962 total revolutions in the first 10 seconds.

Is that correct?

Thanks

 

[stockzahn]

Yes, correct solution. But instead of

Over the first 3.97 s, it the angular velocity increases linearly, so the average is 120 rps/2 = 60 rps.

you could have calculated it with $φ=\ddot{φ}\frac{t^2}{2}$.