How should I attempt this question:

"A computer hard disk starts from rest, then speeds up with an angular

acceleration of 190 rad/s2

until it reaches its final angular speed of

7 200 rpm. How many revolutions has the disk made 10.0 s after it starts

up? (Hint: it stops accelerating before 10.0 s pass.) "

You need to divide this problem into two parts

first part is when it was accelerating ... that time use the equation of motion and calculate what is the total angle covered and hence you get the number of revolutions

then find the time of acceleration ... so you ll understand for how much did you do the above calculation

for the rest of the time, the speed is constant (final angular speed) ... so now you just use

w = theta / time ... and get theta and again calculate the number of revolutions!