Why Does My Physics Book Use L/2 for Calculating Linear Acceleration?

[UrbanXrisis]

The sample problem in my physics book that I do not understand is http://home.earthlink.net/~urban-xrisis/clip001.jpg

The only thing that I do not understand is the LAST sentance...

For example,the middle of the rod has an acceleration of 3g/4

I'm pretty sure that they are talking about the centripetal acceleration but they do not show how they got it. The book stops there. Any ideas of how they got 3g/4?

 

[dextercioby]

Yes,$$\alpha=\frac{3g}{2L}$$

.So for the middle of the rod,the linear acceleration is:

$$a=\alpha\times\frac{L}{2}$$

which gives the answer you asked about.

Daniel.

 

[UrbanXrisis]

why was (L/2) used for the original equation that asked for the linear acceleration of the whole rod?

 

[Doc Al]

why was (L/2) used for the original equation that asked for the linear acceleration of the whole rod?

What equation are you referring to? While the rod has a single angular acceleration, the linear acceleration varies along the length (as Daniel illustrated): $a = \alpha R$, where R is the distance from the pivot.

L/2 is used in determining the torque due to the weight of the rod, which acts at the center of mass.