JEE Main 2024 Question Paper Solution Discussion Live JEE Main 2024 Question Paper Solution Discussion Live

Dimensions of Rotational Kinetic Energy

Dimensional Formula of Rotational Kinetic Energy

The dimensional formula of Rotational Kinetic Energy is given by,

M1 L2 T-2

Where,

  • M = Mass
  • L = Length
  • T = Time

Derivation

Rotational Kinetic Energy (R.Ke) = 2-1 × [Moment of Inertia] × [Angular velocity].  . . . (1)

Since, the moment of inertia (MOI) = Mass × (Radius of Gyration)2

∴ The dimensions of MOI = M1 LT0 . . . . . (2)

And, angular velocity = Δθ × t-1

∴ the dimensional formula of angular velocity = [MLT-1] . . . .(3)

On substituting equation (2) and (3) in equation (1) we get,

Rotational Kinetic Energy = 2-1 × [Moment of Inertia] × [Angular velocity]2

Or, R.Ke = [M1 LT0] × MLT-1]= [M1 L2 T-2].

Therefore, rotational kinetic energy is dimensionally represented as [M1 L2 T-2].

⇒ Check Other Dimensional Formulas:

Test your Knowledge on Kinetic energy

Comments

Leave a Comment

Your Mobile number and Email id will not be published.

*

*