Question 683: Centre of Mass and Rotational Motion

Question

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be  in the ratio

Accepted Answer

$$K.E. = {1 \over 2}I{\omega ^2}$$
$$ 	herefore {1 \over 2}{I_1}\omega _1^2 = {1 \over 2}.2{I_1}\omega _2^2$$
$${{\omega _1^2} \over {\omega _2^2}} = {2 \over 1} \Rightarrow {{{\omega _1}} \over {{\omega _2}}} = {{\sqrt 2 } \over 1}$$

Answer

2 : 1

Answer

1 : 2

Answer

$$\sqrt 2 :1$$

Answer

$$1:\sqrt 2 $$

Centre of Mass and Rotational Motion

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio

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