Question

0
For a system of N particles, show that the moment of inertia of depends upon
(i) individual masses and
(ii) the distribution of these masses about the given axis of rotation.​

Answer 1

• Moment of Inertia is the measure of the rotational inertia of a body.

• The moment of inertia depends on the distribution of mass around an axis of rotation.
• Inertia is the resistance to change in linear motion, similarly moment of inertia is a property of a body due to which it resists angular acceleration that is rotational motion.
• Moment of inertia is the sum of the product of mass of each particle with its square of a distance from its axis of rotation.
• The formula of Moment of Inertia is expressed as I = Σ miri²
• For a system of N particles, moment of inertia will be:

I= m₁r₁² + m₂r₂² + m₃r²........mₙrₙ²

I =  Σ mₙrₙ²

The moment of inertia for a system of particle, depends on the individual masses and the distribution of these masses about the axis of rotation.

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