The rotational inertia (moment of inertia, $I$) of a spinning body can be calculated using the relationship between angular momentum ($L$) and angular velocity ($\omega$):

$L = I \cdot \omega$

Rearranging for $I$:

$I = \frac{L}{\omega}$

Given:

• $L = 100 \, \text{kg·m}^2/\text{s}$
• $\omega = 1.61 \, \text{rad/s}$

Substitute the values:

$I = \frac{100}{1.61} \approx 62.11 \, \text{kg·m}^2$

Final Answer:

The rotational inertia of the spinning body is approximately 62.11 kg·m².

Would you like a detailed explanation of the derivation or the significance of this formula?

Relative Questions:

1. What is the relationship between rotational inertia and torque in rotational motion?
2. How does angular momentum depend on both mass distribution and angular velocity?
3. What are practical examples of calculating rotational inertia in daily life?
4. How does changing angular velocity affect angular momentum for a constant rotational inertia?
5. Can you explain the physical significance of the moment of inertia in rotational dynamics?

Tip:

Rotational inertia depends not only on the mass of the body but also on the distribution of the mass relative to the axis of rotation.