Rigid-Body Work and Energy- Example Problem 8.5-4

 

An 80-lb sphere (r = 1.5 in) is attached to a 20-lb slender rod (L = 3 ft) shown, which is pinned at point O. At the instant the pendulum is vertical, the rod has an angular velocity of ω = 0.5 rad/s. Determine the angle θ to which the rod swings before it momentarily comes to rest.

 

 

Given:

• W_s = 80 lb
• W_r = 20 lb
• r = 1.5 in
• L = 3 ft
• ω₁ = 0.5 rad/s
• ω₂ = 0
• θ₁ = 0
• state 1 = when θ = 0
• state 2 = when the system momentarily comes to rest

 

Find:

• θ₂

 

Video solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Interactive solution:

 

Determine the overall center of mass for the system. What is the mass center's location from the axis through O?

 

y_G = ft