A mass held by a bar with negligibly small mass is freely ro

A mass held by a bar with negligibly small mass is freely routing (torque on the shaft is zero) on a vertical plane. Assume that m = 10 lb and r = 18 in. The tangential speed of the mass at the position shown in the diagram is 10 fps. What is the direction of the acceleration?

Solution

Since the mass has no torque and thus no angular acceleration and thus no tangential acceleration.

Also it possess a velocity and thus the centripetal acceleration acts towards the direction F (inwards towards the center).

Also, the acceleration due to gravity acts in the vertically downwards direction in the direction of D.

Thus there are two components of acceleration, one along F and one along D. therefore, the resultant acceleration acts towards the direction E.