The 30-in. slender bar weighs 20 lb and is mounted on a vertical shaft at O. If a torque lb-in. is applied to the bar through its shaft, calculate the horizontal force R on the bearing as the bar starts to rotate.

Complete Question:

The 30-in. slender bar weighs 20 lb and is mounted on a vertical shaft at O. If a torque, M = 100 lb-in. is applied to the bar through its shaft, calculate the horizontal force R on the bearing as the bar starts to rotate.

The attached diagram completes the question

α = 23.02 rad/s²

Explanation:

From the Free Body Diagram attached to this solution:

...............(1)

Substitute Ic and m into equation (1)

W = 20 lb

l = 30 in = 30/12 ft = 2.5 ft

g = 32.2 ft/s²

d = 3 in = 3/12 ft = 0.25 ft

Taking moment about O

M = 100 lb-in = 100/12 lb - ft = 8.33 lb - ft

8.33 = 0.362 α

α = 8.33/0.362

α = 23.02 rad/s²