# Angular acceleration

## 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
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
Homework Helper
Gold Member
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}##.

• lekh2003