Question
Angular momentum $L$ and rotational kinetic energy $K_{R}$ of a rigid body are related to each other by the relation. (I = moment of inertia)(a) $K_{R}=2 I L$(b) $K_{R}=\frac{L^{2}}{2 I}$(b) $K_{R}=\frac{2 I}{L}$(d) $K_{R}=\frac{L^{2}}{I}$
Step 1
Step 1: The angular momentum $L$ of a rigid body is given by the formula $L = I \omega$, where $I$ is the moment of inertia and $\omega$ is the angular velocity. Show more…
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Rotational kinetic energy (K) and angular momentum (L) are related as (a) $\mathrm{K}^{2}=2 \mathrm{IL}$ (b) $\mathrm{L}=2 \frac{\mathrm{I}}{\mathrm{K}}$ (c) $\mathrm{L}^{2}=2 \mathrm{IK}$ (d) $\mathrm{L}^{2}=2 \frac{\mathrm{I}}{\mathrm{K}}$
Angular momentum of a rigid body about a fixed axis is given by $$L=1 \omega$$ where $I$ is moment of inertia and $\omega$ is angular velocity about that axis. Kinetic energy of body is given by $$ \begin{array}{ll} & K=\frac{1}{2} / \omega^{2} \\ \therefore \quad & K=\frac{1}{2 I}(\mid \omega)^{2}=\frac{L^{2}}{21} \\ \Rightarrow \quad & I=\frac{L^{2}}{2 K} \end{array} $$
Gravitation
Round 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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