The rectangular plate of uniform small thickness with mass of m kg is welded at

Question

The rectangular plate of uniform small thickness with mass of m kg is welded at the theta angle to the midpoint of a vertical shaft of length L and rotating at constant angular velocity of omega rad/s. Define your coordinate system and determine the angular momentum H of the plate about O and find the kinetic energy of the plate. the moment M applied to the shaft by the plate due to dynamic imbalance, and the reaction forces at both bearing supports (neglect gravitational force) at the instant shown.

Explanation / Answer

1. moment of inertia for the slab = (1/12)m(a2 + b2). Therefore H= I*w (w= angular velocity).

H= (1/12)*m*(a2 + b2)*w. Similarly K.E. = (1/2)* (1/12)*m*(a2 + b2)*w2?.

2. Taking the system as plate, since ang. momentum remains conserved, external torque = 0.

3. since moment on plate due to shaft = 0, therefore force on bearings = 0 also .

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