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For a system, the moment of inertia (I) vs. angular velocity (ω) graph looks like:
Question

For a system, the moment of inertia (I) vs. angular velocity (ω) graph looks like:

A.

Rectangular hyperbola

B.

Sigmoidal

C.

Straight line passing through origin

D.

Exponential

Correct option is A

The Correct Answer is: (a) Rectangular hyperbola
Explanation:
In rotational motion, angular momentum (L) is given by the relation:
L = IωI \cdot \omega​​
If angular momentum (L) is kept constant, then the moment of inertia III and angular velocity ω are inversely proportional to each other:
I1ωI \propto \frac{1}{\omega}​​
This is the equation of a rectangular hyperbola. Thus, a graph of I vs. ω (for constant angular momentum) will be a rectangular hyperbola.
Information Booster:
  • Moment of Inertia (I): Measures a body's resistance to change in rotational motion.
  • Angular Velocity (ω): Rate of rotation of an object per unit time.
  • Under constant torque ,Iω,I \propto \omega, producing a linear graph.
  • Rotational Kinetic Energy: KE = 12Iω2\frac{1}{2}I\omega^2​​
  • Moment of Inertia depends on mass distribution and axis of rotation.

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