Using torque to find the speed of a wheel?

Question

a grinding wheel is in the form of a uniform solid disk of radius 6.94cm and a mass of 2.06kg. it starts from rest and accelerates uniformly under the action of the constant torque of 0.606N*m that the motor exerts on the wheel.

how long does the wheel take to reach its final operating speed of 1200 rev/min?

through how many revolutions does it turn while accelerating?

Answer 1

I=m*r^2/2
T=I*alpha

we have enough to compute alpha
0.606=(2.06*.0694^2/2)* alpha
alpha=122 rad/s^2

I rev=2*pi rad
I min=60 sec
w=alpha*t
1200 rev/min=
1200*2*3.14/60 rad /sec
125.6 seconds

th=.5*alpha*t^2
although for this starting from rest under constant acceleration the average speed is
600 rev/min
or 10 rev/sec

so the revs are
1256
j