| Leon |
How do I calculate the moment of inertia, I, of a solid sphere of mass M and radius R, about its line of symmetry? I=òr2 dr I is supposed to be 2MR2/5 |
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| Arun
Iyer |
The sphere you are talking about is the solid sphere. The method i know of starts by finding moment of inertia of a hollow sphere and then using that result to find the moment of inertia of the solid sphere.(prolly a very tedious but understandable method) Do you know how to calculate the moment of inertia of a hollow sphere??If no write back and i(or some of the other Nrich members) would help you out!!!(However i might delay my posts due to obscure schedule so please excuse me if i post late) love arun |
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| Stephen Burgess |
The sphere is symmetrical. Therefore: I=òx2+y2 dx dy dz by calculating the MoI parallel to the z-axis. Also, I=òy2+z2 dx dy dz and I=òx2+z2 dx dy dz by symmetry. So 3I=ò2(x2+y2+z2) dx dy dz I=2/3òr2 dx dy dz I=2/3òr2 dr dqdf×r2sinq (where r, q and f are standard spherical polar co-ordinates). Calculating the integral gives I=8p/15 r4, M=4/3pr3 so I=2/5 Mr2. You can do the integral directly, but using the symmetry argument makes the maths slightly easier. Steve |