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In this lesson, we will learn how to find the radius of gyration by using the moment of the inertia.

Q1:

A uniform ring of radius π and mass π has a particle of mass π attached to it. Find the moment of inertia of the composite body about an axis passing through the centre of the ring and perpendicular to the plane of the ring.

Q2:

Matthew has a model train that uses a circular cone as a flywheel. The cone has radius π and height β .

Find its moment of inertia about its axis of symmetry.

What is its radius of gyration about this axis?

Matthew would like to replace the cone with a circular cylinder of the same mass. He does not want this change to affect the performance of his train, so he needs a cylinder with the same moment of inertia as the cone. Find an expression for the radius π of the cylinder that he needs to buy.

Q3:

Find the moment of inertia of a uniform solid sphere of radius π and mass π about a chord of the sphere which lies at a distance β 2 π 2 from the centre of the sphere.

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