The moment of inertia of a circular disc around its axis will be directly proportional to its mass if the radius remains unchanged. This means that as the mass of the circular disc increases, its moment of inertia will also increase.
The moment of inertia of a circular disc can be calculated using the following formula:
I = (1/2) * m * r^2
where I is the moment of inertia, m is the mass of the circular disc, and r is its radius. As the radius remains constant in this case, the moment of inertia will be proportional to the mass. This means that if the mass of the circular disc is doubled, its moment of inertia will also double, and if the mass is tripled, the moment of inertia will be tripled, and so on.
In other words, if we increase the mass of the circular disc without changing its radius, its moment of inertia will increase proportionally. This is because the moment of inertia measures the resistance of an object to rotational motion, and a heavier object will naturally have more resistance to rotational motion than a lighter object with the same size and shape.
