The moment of inertia of a semi-circular disc about an axis perpendicular to the plane of the disc and passing through its center can be calculated using the formula for the moment of inertia of a full disc and then dividing by 2, since a semi-circular disc is half of a full disc.

Here are the steps:

1. The moment of inertia (I) of a full disc is given by the formula I = 1/2 * m * r^2, where m is the mass of the disc and r is the radius.

2. Since a semi-circular disc is half of a full disc, its moment of inertia would be half of the moment of inertia of a full disc. Therefore, the moment of inertia of a semi-circular disc is given by I = 1/2 * (1/2 * m * r^2).

3. Simplifying the above expression gives I = 1/4 * m * r^2.

So, the moment of inertia of a semi-circular disc about an axis perpendicular to the plane of the disc and passing through its center is 1/4 * m * r^2.

Question

The moment of inertia of a semi-circular disc about an axis perpendicular to the plane of the disc and passing through its center can be calculated using the formula for the moment of inertia of a full disc and then dividing by 2, since a semi-circular disc is half of a full disc.

Here are the steps:

1. The moment of inertia (I) of a full disc is given by the formula I = 1/2 * m * r^2, where m is the mass of the disc and r is the radius.

2. Since a semi-circular disc is half of a full disc, its moment of inertia would be half of the moment of inertia of a full disc. Therefore, the moment of inertia of a semi-circular disc is given by I = 1/2 * (1/2 * m * r^2).

3. Simplifying the above expression gives I = 1/4 * m * r^2.

So, the moment of inertia of a semi-circular disc about an axis perpendicular to the plane of the disc and passing through its center is 1/4 * m * r^2.

Knowee AI · Accepted Answer

The moment of inertia of a semi-circular disc about an axis perpendicular to the plane of the disc and passing through its center can be calculated using the formula for the moment of inertia of a full disc and then dividing by 2, since a semi-circular disc is half of a full disc.

Here are the steps:

1. The moment of inertia (I) of a full disc is given by the formula I = 1/2 * m * r^2, where m is the mass of the disc and r is the radius.

2. Since a semi-circular disc is half of a full disc, its moment of inertia would be half of the moment of inertia of a full disc. Therefore, the moment of inertia of a semi-circular disc is given by I = 1/2 * (1/2 * m * r^2).

3. Simplifying the above expression gives I = 1/4 * m * r^2.

So, the moment of inertia of a semi-circular disc about an axis perpendicular to the plane of the disc and passing through its center is 1/4 * m * r^2.

moment of inertia of a semi circular disc

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