Is r=L Always Valid for Centripital Force and Velocity in Circular Motion?

[Abhishekdas]

Circular motion...

Homework Statement

If a wire has some length and a any random abject is attached to it and we whirl it around in a cirle...this object has finite(non negligible dimentions)...Lets say we know the distance of the point of suspension from the centre of mass of this body(let it be L)...
Now for centripital force mw²r can we take this r=L? If so why? and can we then say v(vel of CM)=Lw?

Homework Equations

The Attempt at a Solution

 

[gneill]

Why don't you try a simple example and see what happens? Say you have a short, thin, uniform but heavy rod of mass M and length a. Determine the linear mass density. Now, suppose your wire is attached to one end of this rod and it's set spinning as you suggest. Calculate the tension in the wire for a given rotational velocity (it'll require an integration over the length of the rod). See if it matches the value you get of you assume all the mass is at the center of mass of the rod.

 

[Abhishekdas]

Hi...
it comes out to be true in this case...But is it a proven thing in physics?...

We know that net force acting in a body = ma here a = acc of CM...this is a property of CM...stnadard result...
now here Tension = m*acceleration of CM...her acc of CM is mw^2*L...

So it should be true for all bodies in general...So is this a valid proof(using the standard result) for the fact that in mw^2*r we can always take the r as the dist of point of suspension from the centre of mass? Does that answer my question...

I mean it is sudddenly getting clear to me and i am pretty sure its always true(i didnt think of the standard result in that way...)...