- #1
yttuncel
- 28
- 0
Homework Statement
A dumbbell is made of a rod length L and mass M, and 2 spheres of radius r and mass m (see figure). The rod is attached at a distance L/3 from the left end to a
rotational axis A. The dumbbell is let go under gravity and makes a rotational motion under gravity around the rotational axis A. (Known: g, M, m, L, r)
a) Make a detailed analysis of the problem
b) Find the distance between the center of mass of the system and the rotational axis A.
c) Find the moment of inertia (I) of the system about A.
d) What is the maximum angular velocity achieved by the system?
e) What are the maximum speed of each of the spheres?
http://imageupload.org/thumb/thumb_145674.jpg
Homework Equations
I=MR2
xcm=(Ʃmx)/M
The Attempt at a Solution
b) I don't get what it meant, shall i say L/6 directly or anything else? Compute center of mass from the formula? But how?
c) I found an answer from parallel axis theorem. That is:
I=2/5mr2+m(r+L/3)2+2/5mr2+m(r+2L/3)2+1/12ML2+1/36ML2
Currently I am at the d) part, please comment and help :)