I = (1/2) * m * r²
Where:
* I is the moment of inertia
* m is the mass of the disk
* r is the radius of the disk
Explanation:
The moment of inertia is a measure of an object's resistance to rotational motion. It depends on the mass distribution of the object relative to the axis of rotation.
For a circular disk, the mass is evenly distributed across its area. The formula above is derived using calculus and represents the sum of the individual moments of inertia of all the infinitesimally small mass elements that make up the disk.
Key Points:
* The moment of inertia is directly proportional to the mass of the disk. A larger mass means more resistance to rotation.
* The moment of inertia is also directly proportional to the square of the radius. A larger radius means a greater distance between the mass elements and the axis of rotation, leading to increased resistance to rotation.
Example:
Let's say we have a circular disk with a mass of 1 kg and a radius of 0.5 m. The moment of inertia would be:
I = (1/2) * 1 kg * (0.5 m)² = 0.125 kg⋅m²
