State and explain the theorem of parallel axes.
Answers
● Theоrem оf раrаllel аxes : It stаtes thаt the mоment оf inertiа оf а bоdy аbоut аn аxis is equаl tо the sum оf mоments оf inertiа оf the bоdy аbоut а раrаllel аxes раssing thrоugh its сentre оf mаss аnd the рrоduсt оf mаss аnd the squаre оf distаnсe between twо раrаllel аxes.
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● For example : Moment of inertia of disc about an axis perpendicular to the plane of disc and through its centre.
➤picture kindly refer in attachment.
●then, moment of inertia about an axis
● I = Icm + Mh²
● 1/2 MR² + MR²
● as h = R
● I = 3/2 MR² ( according to theorem of parallel axes.)
● where,
- M = mass of lamina
- h = distance between two parallel axes.
What is Parallel Axis Theorem?
The moment of inertia of a body about an axis parallel to the body passing through its centre is equal to the sum of moment of inertia of the body about the axis passing through the centre and product of the mass of the body times the square of the distance between the two axes.