derivation of moment of inertia from the sum of torques and sum of forces equation is I=mr(g-rα(net)/ α(fr) + α(net)
In physics, a moment of inertia is a quantitative measure of a body's rotational inertia—that is, the body's resistance to having its speed of rotation about an axis altered by the application of a torque (turning force).
Torque on system = (mg) x r - (m xa)x r -
a = rα(net) (the relationship between linear and rotational acceleration)
SO, T = mgr - mr2 α(net)
Torque is also given by T = I α
here α =α(fr) + α(net)
Hence α(fr) + α(net)= mgr - mr2 α(net)
I=mr(g-rα(net)/ α(fr) + α(net)
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