a grinding wheel of mass 2kg and radius 35 cm can be thought of as a soild disk.

Question

a grinding wheel of mass 2kg and radius 35 cm can be thought of as a soild disk. the disk is initially at rest and then experience a constant acceleration for 11 seconds until it reaches operating speed 700 r.p.m

1- what torque was applied to the wheel?
2- what was the wheen anguler displacement during this time?


2- suppose people could consume gasoline as a food source. A typical gallon has a mass of 3.2 kg and provides 44 kj per gram of energy.
a- yout metabloic power for running at 15km/h is 1150 w how far could you run in a gallon of gasoline?

Explanation / Answer

torque = I*alpha

I =moment of inertia of solid disk = MR^2/2 = 2*(0.35m)^2/2 = 0.1225

wf = wi + alpha*t

wi = 0

t = 11 s

wf = 700 rpm = 73.3 rad/s

alpha = wf/t

alpha = 6.664 rad/s^2

torque = 0.81634 N-m

part b )

theta =wi*t + 1/2 *alpha*t^2

theta = 403.172 rad

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