Setting Up KE for 2 Point Masses and a Rod

[Reshma]

Two point masses are joined by a rigid weightless rod of length "l", the centre of which is constrained to move on a circle of radius 'a'. Set up the kinetic energy in generalised coordinates.

So in this case, since the 2 mass m are joined by a rod, I consider the reduced mass of the system $\mu$:
$${1\over {\mu}} = {1\over m} + {1\over m}$$
$$\mu = {m\over 2}$$

Am I going right? How do I set up the KE in this case?

 

[OlderDan]

Two point masses are joined by a rigid weightless rod of length "l", the centre of which is constrained to move on a circle of radius 'a'. Set up the kinetic energy in generalised coordinates.

So in this case, since the 2 mass m are joined by a rod, I consider the reduced mass of the system $\mu$:
$${1\over {\mu}} = {1\over m} + {1\over m}$$
$$\mu = {m\over 2}$$

Am I going right? How do I set up the KE in this case?

It's not clear to me that the reduced mass will be helpful. I think you need to pick your generalized coordinates. It looks to me like a pair of angles would be a natural choice.

 

[Reshma]

Pair of angles? I don't get it . I can consider one angle i.e. the polar angle on the circle but what is the other angle?

 

[George Jones]

Pair of angles? I don't get it . I can consider one angle i.e. the polar angle on the circle but what is the other angle?

If the rod is free to rotate about its centre, then another angle is need. This could be, for exampe, the angle that the rod makes with respect to horizontal, or the angle that the rod makes with respect to the line (radius) that joins the centre of the rod to the centre of the circle.

Some choices make the analysis easier than other choices.