A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is fre

Question

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 250 N applied to its edge causes the wheel to have an angular acceleration of 0.991 rad/s2.
(a) What is the moment of inertia of the wheel?
kg · m2

(b) What is the mass of the wheel?
kg

(c) If the wheel starts from rest, what is its angular velocity after 4.00 s have elapsed, assuming the force is acting during that time?
rad/s

Explanation / Answer

torque T = 250x0.33 = 82.5 N-m angular acceleration a = 0.991 1) => moment of inertia I = 82.5/0.991 = 83.25 kg-m2 2) mr^2/2 = I = 83.25 => m = 83.25/0.33^2 x2= 1528.92 kg 3) ?= at = 0.991x4 = 3.964 rad/s

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