A grinding wheel is a uniform cylinder with a radius of 8.70 cm and a mass of 0.400 kg.
a)calculate the moment of inertia about the center.
b)Calculate the applied torque needed to accelerate it from rest to 1950 rpm in 6.00 s if it is known to slow down from 1250 rpm to rest in 57.5 s.
The Attempt at a Solution
first i changed the given radius to .087 m..
a) wasnt that hard, I=mR^2, (.4)(.087)^2=.00151
b) since i was given the ωi=0, and ωf=1950 rpm→32.5 rps, and t=6s, i used the formula ωf=ωi+αt, and got α=5.42. i used my α to solve for a with the equation a=Rα (because F=ma) and got .47, then using F=ma, F=(.4)(.47)=.19. Since τ=RF, τ=(.19)(.087)=.02, which is incorrect.
Im guessing that my calculated I has something to do with the answer because of the way my professor asks the question, in parts where you use your answer in part a to solve for part b which is needed to solve for part c, etc, but i dont understand how my answer is wrong. however realistically i can understand how a τ of .02 wouldnt cause a cylinder to rotate from 0 to 1950 rpm in 6 sec.