A grindstone in the form of a solid cylinder has a radius of .5m and a mass of 50kg. (a) What torque will bring it from rest to an angular velocity of 300 rev/min in 10s. (b) What is its kinetic energy when it is rotating at 300 rev/min. I will do (b) first: w = 300 rev/min = 5 rev/s w = 10*pi rad/s K.E., = .5*I*w^2. Where I = .5*m*R^2...i.e., the moment of inertia. Therefore, K.E., = 5000*pi^2/16 = 3084J. (a) P=T*w; T const'. Where P = power, T=torque, w=angular velocity. (Also work = T*(theta2 - theta1)). But this is only the power for a particular value of w, what is the power when w<300rev/min, e.g., 200, 100, etc., rev/min. We want to find the total amount of K.E., for w=0 to w=300 rev/min interval. Is there an integral some where here, and what is it? Many thanks. P.S. Currently on the 2nd page of this thread I got a 2nd question on angular velocity, I hope some one will be able to answer it for me. Thanks again.