Question

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.

Answer 1

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

Answer:

α = 23.02 rad/s²

Explanation:

From the Free Body Diagram attached to this solution:

$I_{0} = I_{c} + md^{2}$...............(1)

$I_{c} = \frac{ml^{2} }{12} \\W = mg, m = W/g$

Substitute Ic and m into equation (1)

$I_{0} =\frac{ml^{2} }{12} + md^{2}\\I_{0} =\frac{Wl^{2} }{12g} + \frac{Wd^{2}}{g}$

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

$I_{0} =\frac{20 * 2.5^{2} }{12*32.2} + \frac{20*0.25^{2}}{32.2}\\I_{0} = 0.362 lb-ft-s^2$

Taking moment about O

$\sum M_{0} = I_{0} \alpha$

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