5/2 I.. I = mr²/2, nd th' diam, MI is mr²/4..nd so, th' tangent in its own plane..MI= mr²/4+mr²= 5/4 m r².. so 5/2 I.

Moment of inertia of a disc about its own axis is I. Its moment of inertia about a tangential axis in its plane can be calculated using the parallel axis theorem. The parallel axis theorem states that the moment of inertia of a body about any axis parallel to and a distance 'd' away from an axis through its center of mass is equal to the sum of the moment of inertia about the center of mass and the product of the mass of the body and the square of the distance 'd'.

Parallel Axis Theorem:
The moment of inertia I' of a body about an axis parallel to and a distance 'd' away from an axis through its center of mass is given by the equation:

I' = I + md²

where:
- I is the moment of inertia of the body about an axis through its center of mass
- m is the mass of the body
- d is the distance between the two parallel axes

Explanation:
When a disc rotates about its own axis, the moment of inertia is given by the equation I = (1/2)MR², where M is the mass of the disc and R is its radius.

When considering a tangential axis in the plane of the disc, which is a distance 'd' away from the axis through its center of mass, the moment of inertia I' can be calculated using the parallel axis theorem.

The moment of inertia of the disc about its own axis (I) is (1/2)MR².

Using the parallel axis theorem, the moment of inertia about the tangential axis (I') is given by the equation:

I' = I + md²

Since the mass of the disc is constant, we can simplify the equation to:

I' = (1/2)MR² + Md²

Simplifying further, we get:

I' = (1/2)MR² + M(d²)

I' = (1/2)MR² + (Md²)

I' = (1/2)MR² + (1/2)MR²

I' = MR²

Therefore, the moment of inertia of a disc about a tangential axis in its plane is equal to MR².

Summary:
The moment of inertia of a disc about its own axis (I) is (1/2)MR². The moment of inertia about a tangential axis in its plane (I') is equal to MR², according to the parallel axis theorem.