If I is the moment of inertia and ωthe angular velocity, what is the dimensional formula of rota

step 1 Dear students, in problem 50 of chapter 1st we have asked that if i is the momentum of inertia a

If I is the moment of inertia and ωthe angular velocity,...

If $I$ is the moment of inertia and $\omega$ the angular velocity, what is the dimensional formula of rotational kinetic energy (a) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]$ (b) $\left[\mathrm{M}^{2} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right]$ (c) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$ (d) $\left[\mathrm{M}^{2} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right]$

If $I$ is the moment of inertia and $\omega$ the angular velocity, what is the dimensional formula of rotational kinetic energy
(a) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]$
(b) $\left[\mathrm{M}^{2} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right]$
(c) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$
(d) $\left[\mathrm{M}^{2} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right]$

Key Concepts

Rotational Kinetic Energy

Rotational kinetic energy refers to the energy an object possesses due to its rotation, typically calculated by the formula E = ½ I?², where I is the moment of inertia and ? is the angular velocity. By combining the dimensions of moment of inertia ([ML²]) with the square of angular velocity ([T?²]), the resulting dimensional formula for rotational kinetic energy is [ML²T?²], aligning with the dimensions of energy in general.

Angular Velocity

Angular velocity measures the rate of rotation of an object, defined as the angle turned per unit time. Its dimensional formula is [T?¹], indicating that it fundamentally involves the inverse of time, and it is pivotal in describing rotational dynamics.

Moment of Inertia

Moment of inertia quantifies a body's resistance to angular acceleration around a given axis and depends on the mass distribution relative to that axis. Dimensionally, it is represented as mass multiplied by the square of length, commonly expressed as [ML²].

Dimensional Analysis

Dimensional analysis is a method used to deduce the relationships among different physical quantities by expressing them in terms of their fundamental dimensions, such as mass (M), length (L), and time (T). It helps verify that equations are dimensionally consistent and can assist in deriving formulas or checking the correctness of physical equations.

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