If L is the angular momentum and I is the moment of inertia of a rotating body, then `(L^(2))/(2I)` represents its

Options

A. Rotational K.E.
B. Total energy (c)
C. Rotational P.E.
D. Translational K.E.

Explanation

To solve the problem, we need to analyze the relationship between angular momentum (L), moment of inertia (I), and rotational kinetic energy.

### Step-by-Step Solution:

1. **Understanding Angular Momentum**:
The angular momentum (L) of a rotating body is given by the formula:
\[ L = I \cdot \omega \]
where \(I\) is the moment of inertia and \(\omega\) is the angular velocity.

2. **Expressing Angular Momentum in Terms of \(\omega\)**:
From the equation above, we can express \(L\) in terms of \(\omega\):
\[ L = I \cdot \omega \]

3. **Calculating \(L^2\)**:
To find \(L^2\), we square the expression for \(L\):
\[ L^2 = (I \cdot \omega)^2 = I^2 \cdot \omega^2 \]

4. **Finding \(\frac{L^2}{2I}\)**:
Now, we substitute \(L^2\) into the expression \(\frac{L^2}{2I}\):
\[ \frac{L^2}{2I} = \frac{I^2 \cdot \omega^2}{2I} \]

5. **Simplifying the Expression**:
We can simplify the expression:
\[ \frac{L^2}{2I} = \frac{I \cdot \omega^2}{2} \]

6. **Identifying the Result**:
The expression \(\frac{I \cdot \omega^2}{2}\) is recognized as the formula for rotational kinetic energy (\(K.E_{rot}\)):
\[ K.E_{rot} = \frac{1}{2} I \omega^2 \]

Thus, we conclude that:
\[ \frac{L^2}{2I} = \text{Rotational Kinetic Energy} \]

### Final Answer:
\(\frac{L^2}{2I}\) represents the rotational kinetic energy.

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