A uniform solid disk of radius $50$ cm and mass $10$ kg is used as a grinding wheel. The motor exerts a constant torque of $2\mathrm{.}5$ Nm on the wheel. If it starts from rest and accelerates uniformly.

Given: moment of inertia for a disk $I=\frac{1}{2}M{R}^2$

$($a$)$ how long does the wheel take to reach its final operating speed of $600re\frac{v}{?}$ min?

$($b$)$ through how many revolutions does it turn while accelerating?

$8.$ A rectangular slab of ice floats on water with a large portion submerged beneath the water surface. The volumer of the slab is $20m^3$ and the surface area of the top is $14m^2.$