- #1
Ja4Coltrane
- 225
- 0
I'm wondering how you would prove the (2/3)MR^2 moment of inertia of a hollow sphere.
My idea was to brake it into like...sort of cylindrical shells. ones with that are very very short, like little wires making a hollow sphere.
I=int[(r^2)dm]
I=[M/(4pi(R^2))]int[(R^2-y^2)(2pi(R^2-y^2)^.5)dy]
I=[M/(2R^2)]int[(R^2-y^2)^(3/2)dy]
I am just in high school so I won't follow if you guys do anything like a double integral, so if there is a way around that, tell me that way. Thanks!
My idea was to brake it into like...sort of cylindrical shells. ones with that are very very short, like little wires making a hollow sphere.
I=int[(r^2)dm]
I=[M/(4pi(R^2))]int[(R^2-y^2)(2pi(R^2-y^2)^.5)dy]
I=[M/(2R^2)]int[(R^2-y^2)^(3/2)dy]
I am just in high school so I won't follow if you guys do anything like a double integral, so if there is a way around that, tell me that way. Thanks!