State perpendicular axis theorem. What is the moment of inertia of a ring of
mass 2 kg and radius 0.5m about an axis passing through its centre and
perpendicular to its plane? Also find moment of inertia about a parallel axis
through its edge.
Answers
Answer:
Explanation:
In physics, the perpendicular axis theorem (or plane figure theorem) can be used to determine the moment of inertia of a rigid object that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two perpendicular axes lying within the plane.
Perpendicular axis theorem states that the moment of inertia of a planar body about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with the perpendicular axis and lying in the plane of the body.
Moment of inertia of axis passing through centre and perpendicular to its plane = MR² = 2×(0.5)² = 0.5kg m²
Moment of inertia of axis parallel to the above axis and passing through the edge can be found out by parallel axis theorem
Moment of inertia = ICM + Md² = ICM + MR²
= MR²+MR² = 2MR² = 2×2×0.5² = 1
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