Optimizing Pendulum Period with Center of Mass Distance

[cd80187]

In Fig. 15-46, a stick of length L = 1.8 m oscillates as a physical pendulum. (a) What value of distance x between the stick's center of mass and its pivot point O gives the least period? (b) What is that least period?

For this problem, I wasn't sure where to start, I would have thought that the answer would be as far away from the center of mass as possible but I wasn't sure how to do it. I know that you have to use the equation Period = 2 x pi x (square root of (Icom/m x g x h) and that mass cancels out, but I don't know where to go from there, thank you in advance for the help

 

[Doc Al]

You have the equation for the period, now express the variables in terms of "x", the distance between center of mass and pivot point. (What you call "Icom" should be the rotational inertia of the pendulum about the pivot point; "h" is the distance from center of mass to pivot point.)

 

[cd80187]

Yeah, I got the question right, I realized that I was forgetting to cancel out the square root. Thank you for the help