Calculating I for a Circular Hoop with Tangential Axis

[missnuss]

Homework Statement

What is the value of I for a circular hoop of mass M and Radius R about an axis that is tangent to the hoop and lies in the hoops plane?

Homework Equations

The Attempt at a Solution

I=2 theta intergral from -R to R, z^2 square root of (R^2 - z^2)dz = theta pi R^4/4 = 1/4 MR^2

 

[Delphi51]

I'm picturing a circle with a vertical line one left side, just touching the circle. If so, I don't think your integral is correct. I don't know what your Z stands for, but I believe you must integrate around the circle (zero to 2 pi) because the linear mass density is m/(2πR) per unit distance all the way round, whereas integrating linearly the mass density is much higher as you approach the sides of the circle. I get a much larger answer than you have. My intuition is telling me the answer should be larger than mR² because a good part of the mass is distance 2R away from the axis. My answer agrees; yours does not.