Define moment of inertia of a body. Give its units and dimensions. Explain the physical significance of moments of inertia.

The moment of inertia of a body is the quantified measure of its resistance to rotational motion about a selected axis. The moment of inertia is dependent on both the mass of the object and how that mass is distributed relative to the axis about which the body rotates. A bigger moment of inertia therefore translates directly into the fact that it will require more effort to either start or stop the body’s rotational motion.

Its unit is kilogram meter squared, kg·m², and has the dimension of mass multiplied by the square of length. In rotational dynamics, it’s an intrinsic property analogous to the concept of mass in linear motion. It indicates how a body responds to the application of torques.

The physical significance of moment of inertia lies in its impact on rotational systems. It influences how easily a body can be rotated or how much rotational energy it can store. For example, a solid sphere has a smaller moment of inertia compared to a hollow sphere of the same mass and radius, as the solid sphere’s mass is distributed closer to the axis.

Moment of inertia is crucial in the design and understanding of systems such as flywheels, turbines, and vehicle wheels. Athletes also use it to control their rotational speeds by changing body positions, which shows the practical importance of the concept.

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