Description
A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 230 N applied to its edge causes the wheel to have an angular acceleration of 0.818 rad/s2.
Explanation & Answer
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(1) τ = Iα
(2) τ = rF
Substituting (2) into (1):
rF = Iα
Solved for I:
I = rF / α
= (0.330m)(230N) / 0.818rad/s²
= 62.1 kg∙m²
Then, the moment of inertia for a solid uniform cylinder is:
I = 0.5mr²
m = 2I / r²
= 2(62.1kg∙m²) / (0.330m)²
= 1141kg
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