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 280 Napplied to its edge causes the wheel to have an angularacceleration of 1.138rad/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 4.80 s have elapsed, assumingthe force 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 4.80 s have elapsed, assumingthe force is acting during that time?
3 rad/s

Explanation / Answer

Radius R = 0.33 m Tangential force F = 280 N angular acceleration = 1.138 rad/s2 Torque = FR               = 93.33 N m (a). moment of inertia of the wheel I = /                                                       = 82.02 rad / s 2 (b). We know I = ( 1/2) M R 2         Mass of the wheel M= 2I / R 2                                         = 1506.33 kg (c). Intitial angular speed = 0 rad / s       Angular speed after t = 4.8s is ' = ? we know from the relation ' = + t                                              = 5.4624 rad / s                                         = 1506.33 kg (c). Intitial angular speed = 0 rad / s       Angular speed after t = 4.8s is ' = ? we know from the relation ' = + t                                              = 5.4624 rad / s

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