What techniques can be used to analyze a rod rotating about the edge of a table?

[worldbook]

A uniform rod of length 4x is rotating about the edge O of the table. (The rod does not fall off the table.) The centre of mass G of the rod is distance x away from O. The rod is making an angle θ with the horizontal.

The only forces present are the weight W of the rod, the normal reaction N of the table on the rod and the frictional force S that prevents the rod from slipping off the table as it rotates. Let the Radial direction point from O to G, and the Transverse direction be anticlockwise.

I apologise for not including a diagram but it should be very quick to sketch.

Question: Would it be appropriate to approach this problem using Newton's 2nd Law and then resolving the equation into radial and transverse components? If so, am I suppposed to be considering the motion of a point on the rod, or the motion of the rod as a whole body?

In particular, are these eqns meaningful??

−m(xω^2)=S−Wsinθ
m(xα)=Wcosθ−N

 

[jbsteele]

Answer: Yes, it would be appropriate to approach the problem using Newton's Second Law and then resolving the equation into radial and transverse components. You should be considering the motion of the rod as a whole body. The equations you have provided are meaningful and can be used to solve the problem. However, you should note that the equation for the transverse direction should include a centrifugal force term.