Question

Q. The moment of inertia of a thin ring of radius R about an axis passing through any diameter is MR²/2
(a) What is the radius gyration of a ring about a axis passing through the centre?

(b) A ring has a diameter 0.20m and mass 1 kg, calculate its M.I about an axis passing through a tangent perpendicular to its plane.​

Answer 1

The moment of inertia of a thin ring of radius R about an axis passing through any diameter is 1 2 12MR2 To find the moment of inertia of the same ring about an axis passing through its center of mass and perpendicular to its plane, which of the following theorem is used and state the theorem. Perpendicular axis theorem. Parallel axis theorem 2. What is the radius of gyration of the ring about an axis passing through its centre of mass and perpendicular to its plane? 3. A thin metal ring has a diameter 0.20 cm and mass 1 kg. Calculate its moment of inertia about an axis passing through any tangent.Read more on

Explanation:

1. perpendicular axis theorem. 2. Moment of inertia of ring, I = mr2 ____(1) Moment of inertia of ring in terms of radius of gyration, I = mk2 ____(2) From eq(1) and eq(2), we get mk2 = mr2 radius of gyration, k = r. 3. I = I0 + ma2Read more on Sarthaks.com - https://www.sarthaks.com/1089976/the-moment-inertia-thin-ring-of-radius-about-an-axis-passing-through-any-diameter-is1-2mr