(a) Draw a free-body diagram for the rod of Figure 12.4. Let the inertia of the rod be negligible compared to \(m_{1}\) and \(m_{2}\).

(b) Would the free-body diagram change if you slide object 2 to the left?

(c) Experiments show that when \(m_{1}=2 m_{2}\) the rod is balanced for \(r_{2}=2 r_{1}\). How is the ratio \(r_{1} / r_{2}\) related to the ratio \(m_{1} / m_{2}\) ?

(d) What would happen if you remove object 1 from the rod?

(e) What would happen if you double the inertia of object 1? 

(f) What would happen if you carefully place a penny on top of object 1? Let the inertia of the two objects be significantly larger than that of the penny. 

(g) Is there a difference between what would happen in parts \(e\) and \(f\) ?

Transcribed Image Text:

Figure 12.4 Unequal weights balance a rod that is suspended off-center. (a) 1 | (9) F pivot forces exerted on rod by weights 2 I F