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Newton's Second Law: Rotatory Version

The moment of...

Question

The moment of inertia of two rotating bodies are I_A and I_B (I_A I_B) and their angular momenta are equal. Which one has greater kinetic energy?

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Solution

L= angular momentum
I = moment of inertia
w = angular velocity
Suppose Ia > Ib
We know that
L = Iw ( formula)
Given angular momenta are equal:
La = Lb
I_a w_a = I_bw_b
w_a/w_b = I_b/I_{a ...................(1)}
this means w_b >w_a
K.E (kinetic energy) = 1/2 * I * w²
KE_a=1/2 * I_a * w_a²
KE_b=1/2 * I_b * w_b²

KE_a/KE_b= I_a * w_a2 / I_b * w_b2
from eq (1)
KE_a/KE_b= w_a/w_{b ................(2)}
so KE of b is graeter with Inetia as Ib

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Newton's Second Law: Rotatory Version

Standard XII Physics

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