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The rotational kinetic eneegy is gicen by 1/2 iomega 2 dimension of i

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student-name Deepali Sharma asked in Physics

the rotational kinetic energy of a body is given by E= 1/2 Iw2, where w is angular velocity of the body. Use this equation to get dimensional formula for I.

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student-name Sushant Abhineet answered this

2174 helpful votes in Physics, Class XI-Science

hi Deepali Sharma ,

Please find below the solution to the asked query:

Given E= 1/2 Iw2

The dimension of omega (w) = v/r

where v= velocity and r = radius

so dimensional formula for v = [LT-1] and r = [L]

so dimensional formula for w = [LT-1] / [L] = [T-1]

as dimensional formula for energy is [ML2T-2]

so I = E/w2 = [ML2T-2]/ [T-1]2

= [ML2T-2]/ [T-2] = [ML2]

Hence the dimensonal formula for I = [ML2]