Derivation of moment of inertia of a ring
Answers
Explanation:
PHYSICS
Calculate the moment of inertia of a thin ring of mass m and radius Rabout an axis passing through its centre and perpendicular to the plane of the ring.
December 26, 2019Saraswati Sankhla
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ANSWER
Remember that in case of continuous mass distribution, we use the
formula I=∫(dm) r2 to find out the moment of inertia of the body. AA is the axis about which
rotation of the ring is being considered
Mass of the ring =M, circumference of the ring =2πR.
Consider a small element of the ring at an angle θfrom a particular reference radius. The element subtends and a particular reference radius. The element subtends an angle dθ at the center.
Length of the element =Rdθ
Mass of the element =(λ Rdθ)
Moment of inertia of the element =(λ Rdθ) R2
Moment of inertia of the ring ∫02π(λ Rd</span><span>θ) R2=MR2