Question

The 25-lb slender rod has a length of 6 ft. Using a collar of negligible mass, its end A is confined to move along the smooth circular bar of radius 32√ ft. End B rests on the floor, for which the coefficient of kinetic friction is μB = 0.28. The bar is released from rest when θ = 30∘.

Determine the angular acceleration of the bar at this instant, measured clockwise.

Answer 1

The question figure and free body diagram is as depicted below

From Newton's Second law,

Now,

where,

acts in the direction of the negative x-axis

acts in a direction making 45 degrees downward to the positive x-axis

acts in a direction making 30 degrees to the left to the positive y-axis

On solving the above equation, we get

Similarly

where,

where,

acts in the direction of the negative x-axis

acts in the direction of the negative y-axis

acts in a direction making 45 degrees downward to the positive x-axis

acts in a direction making 30 degrees to the left to the positive y-axis

On solving equation (1) to (5), we get,

(Ans.)