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## Main Question or Discussion Point

How would I find the center of mass (COM) for a ring of variable density, where the variation in density can be described by a continuous mathematical equation.

The density at each location along the ring is described by a function (d) whose independent variables are radius (r) and angle ([tex]\theta[/tex]), i.e., polar coordinates.

The value of d at each r and [tex]\theta[/tex] is the sum of two functions (d1 and d2) where:

d1 = A sinc([tex]\pi[/tex] r)

where A is a constant

AND

d2 = B sinc([tex]\pi[/tex] z)

where B is a constant

And: z = l + r * cos([tex]\theta[/tex])

where l is a constant

NOTE:

The density at each location along the ring is described by a function (d) whose independent variables are radius (r) and angle ([tex]\theta[/tex]), i.e., polar coordinates.

The value of d at each r and [tex]\theta[/tex] is the sum of two functions (d1 and d2) where:

d1 = A sinc([tex]\pi[/tex] r)

where A is a constant

AND

d2 = B sinc([tex]\pi[/tex] z)

where B is a constant

And: z = l + r * cos([tex]\theta[/tex])

where l is a constant

NOTE:

**THIS IS NOT A HOMEWORK QUESTION**