The moment of inertia of two rotating bodies A and B are IA and .IB ·IA>IB) and their angular mo

The moment of inertia of two rotating bodies A and B are IA...

The moment of inertia of two rotating bodies $\mathrm{A}$ and $\mathrm{B}$ are $\mathrm{I}_{\mathrm{A}}$ and $\left.\mathrm{I}_{\mathrm{B}} \cdot \mathrm{I}_{\mathrm{A}}>\mathrm{I}_{\mathrm{B}}\right)$ and their angular momentum are equal. If their K.E. be $\mathrm{K}_{\mathrm{A}}$ and $\mathrm{K}_{\mathrm{B}}$ respectively then $\ldots$ $\{\mathrm{A}\} \mathrm{K}_{\mathrm{A}}, \mathrm{K}_{\mathrm{B}}$ $\{\mathrm{B}\}\left(\mathrm{K}_{\mathrm{B}} / \mathrm{K}_{\mathrm{A}}\right)>1$ \{C\} $\left(\mathrm{K}_{\mathrm{A}} / \mathrm{K}_{\mathrm{B}}\right)=1$ $\{\mathrm{D}\}\left(\mathrm{K}_{\mathrm{B}} / \mathrm{K}_{\mathrm{A}}\right)=(1 / 2)$

The moment of inertia of two rotating bodies $\mathrm{A}$ and $\mathrm{B}$ are $\mathrm{I}_{\mathrm{A}}$ and $\left.\mathrm{I}_{\mathrm{B}} \cdot \mathrm{I}_{\mathrm{A}}>\mathrm{I}_{\mathrm{B}}\right)$ and their angular momentum are equal. If their K.E. be $\mathrm{K}_{\mathrm{A}}$ and $\mathrm{K}_{\mathrm{B}}$ respectively then $\ldots$
$\{\mathrm{A}\} \mathrm{K}_{\mathrm{A}}, \mathrm{K}_{\mathrm{B}}$
$\{\mathrm{B}\}\left(\mathrm{K}_{\mathrm{B}} / \mathrm{K}_{\mathrm{A}}\right)>1$
\{C\} $\left(\mathrm{K}_{\mathrm{A}} / \mathrm{K}_{\mathrm{B}}\right)=1$
$\{\mathrm{D}\}\left(\mathrm{K}_{\mathrm{B}} / \mathrm{K}_{\mathrm{A}}\right)=(1 / 2)$

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Key Concepts

Angular Momentum

Angular momentum is a conserved quantity in rotational systems that quantifies the motion of a rotating object. It is the product of the moment of inertia and the angular velocity. When two systems have equal angular momentum, differences in their moments of inertia will lead to different angular velocities.

Rotational Kinetic Energy

Rotational kinetic energy is the energy due to the rotation of an object and is calculated as one-half times the moment of inertia multiplied by the square of the angular velocity. For systems with equal angular momentum, the rotational kinetic energy varies inversely with the moment of inertia; a smaller moment of inertia results in a higher angular velocity, hence more kinetic energy.

Moment of Inertia

The moment of inertia is a measure of how much an object resists changes in its rotational motion about an axis. It depends on the mass of the object and how that mass is distributed relative to the axis of rotation. A higher moment of inertia means that, for a given angular momentum, the angular speed will be lower.

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