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Proving Rotational K.E. Formula?

by greswd
Tags: formula, proving, rotational
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greswd
#1
Dec2-12, 02:54 AM
greswd's Avatar
P: 147
The total kinetic energy (as viewed from one inertial frame) of a free, rigid body is the sum of all the infinitesimal kinetic energies of the components that comprise the body.


How do we prove that for a rotating body

[tex]E_k=\frac{1}{2}\left(M_{T} v_{c}^{2} + I_{c} ω^{2}\right)[/tex]
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greswd
#2
Dec2-12, 07:52 AM
greswd's Avatar
P: 147
Where MT stands for the total mass of all the infinitesmal components combined.
mfb
#3
Dec2-12, 08:25 AM
Mentor
P: 12,037
Integrate ##\int \frac{1}{2}v^2 \rho dV## (in other words, kinetic energy = 1/2m^2 for all infinitesimal m) and split v into components from translation and rotation and you will get the correct result.


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