Given the moment of inertia of a disc of mass M and radius R about any of its diameters to 1 be 1/4 MR2, find the moment of inertia about an axis normal to the disc passing through a point on its edge.

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Now, let's tackle your question about the moment of inertia of a disc. Given that the moment of inertia of a disc of mass MM and radius RR about its diameter is 14MR241MR2, we can find the moment of inertia about an axis normal to the disc passing through a point on its edge using the parallel axis theorem.

The parallel axis theorem states that the moment of inertia of a body about any axis parallel to an axis through its center of mass is equal to the sum of the moment of inertia about the parallel axis through the center of mass and the product of the mass of the body and the square of the distance between the two axes.

In this case, the distance between the axis passing through the center (where the moment of inertia is known) and the axis passing through a point on the edge is RR (since the radius of the disc is RR).

So, using the parallel axis theorem, we have:

I=Icenter+Md2I=Icenter+Md2

Where:

• II is the moment of inertia about the axis passing through a point on the edge,
• IcenterIcenter is the moment of inertia about the center axis (which is given as 14MR241MR2),
• MM is the mass of the disc,
• dd is the distance between the two axes, which is equal to RR.

Substituting the known values, we get:

I=14MR2+MR2I=41MR2+MR2

I=14MR2+44MR2I=41MR2+44MR2

I=54MR2I=45MR2

So, the moment of inertia about an axis normal to the disc passing through a point on its edge is 54MR245MR2.

If you need further clarification or assistance, feel free to ask!