Rotational dynamics concept: What is the moment of inertia of a body? Choose the statement that best defines moment of inertia with respect to a specified axis; use this to identify its nature and dependence.
IIT JEE
Physics
Difficulty: Easy
Choose an option
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AA vector equal to mass times angular acceleration
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BA scalar measure of rotational inertia about an axis, equal to Σ(mr²) for point masses
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CThe torque needed to keep angular speed constant
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DThe product of mass and linear velocity
Answer
Correct Answer: A scalar measure of rotational inertia about an axis, equal to Σ(mr²) for point masses
Explanation
Concept and definitionMoment of inertia (I) quantifies a body's resistance to change in its angular velocity about a specified axis.For discrete masses: I = Σ mi ri2; for continuous bodies: I = ∫ r² dm.
Why scalar?About a given axis, I is a scalar multiplier in τ = Iα (rigid body), analogous to mass in F = ma.
Common pitfallsConfusing I with angular momentum (L = Iω) or torque.
Final AnswerA scalar measure of rotational inertia about an axis, equal to Σ(mr²) for point masses