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why the equation of moment of inertia is I=mr^2.we see that most of the teachers can't give this ans
wer.plese explain the answer.why we definite I=mr^2? why not I=mr^3 or r^4 or r^5 and so on?

Hello sabbir,

A small body on a string of length r, that is rotating at angular velocity w, has linear velocity at any moment given by
v = w*r
Observe what happens if we use the above expression for velocity v in the kinetic energy formula
KE = (1/2)*m*v^2 = (1/2)*m*(w*r)^2 = (1/2)*m*r^2*w^2

It was desirable to simplify and have the formula for angular kinetic energy look similar to the linear kinetic energy. So m*r^2 was grouped and renamed I. Now we can write the angular kinetic energy
KE = (1/2)*I*w^2
where I = m*r^2

I hope this helps,


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Steve Johnson


I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.


I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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