A large grinding wheel in the shape of a solid cylinder of radius0.330 m is free

Question

A large grinding wheel in the shape of a solid cylinder of radius0.330 m is free to rotate on a frictionless, vertical axle. Aconstant tangential force of 290 N appliedto its edge causes the wheel to have an angular acceleration of0.913 rad/s2. (a) What is the moment of inertia of thewheel?
1kg·m2

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

(c) If the wheel starts from rest, what is its angular velocityafter 4.40 s have elapsed, assuming theforce is acting during that time?
3 rad/s (a) What is the moment of inertia of thewheel?
1kg·m2

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

(c) If the wheel starts from rest, what is its angular velocityafter 4.40 s have elapsed, assuming theforce is acting during that time?
3 rad/s

Explanation / Answer

             Given that the radius of the solid cylinder is R = 0.330 m               Thetangential force is F = 290 N              The angular accelaration is = 0.913rad/s2     -----------------------------------------------------------------------        The torque on thecylinder is = I                                               R*F= I                  where I is the moment of inertia of the wheel                      then    I = R*F /                                   = -----------Kg.m2                                                                  The moment of inertia of thesolid cyllinderof mass M is I = (1/2)MR2                                                                                          M= 2*I / R2                                                                                              = ------------ kg        From the equation ofmotion the final angular veloity with the initial angularveloctiy 1 = 0 is                                 2 = 1 + *t                                        =0 +  *t                                       =  *t                                       = ---------- rad/s                                                                                          M= 2*I / R2                                                                                              = ------------ kg        From the equation ofmotion the final angular veloity with the initial angularveloctiy 1 = 0 is                                 2 = 1 + *t                                        =0 +  *t                                       =  *t                                       = ---------- rad/s

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