Derive an expression for the kinetic energy of a body of mass (m) rotating uniformly about a given axis - Physics - Work Energy and Power

Question

Derive an expression for the kinetic energy of a body of mass (m)
rotating uniformly about a given axis Show that the rotational
kinetic energy = 1/2M (L/K)^2 Where symbols have their usual
meanings

Sayantan · Accepted Answer

Dear Student,

Now, Angular momentum: L=Iω (i)or, ω2=LI2 (ii)Rot K E=12Iω2or, using (ii)K E=12L2I (iii)Now, from radius of gyrationI=MK2 (iv) where K=radius of gyrationthus plugging this in (iii)Rot K E= 12ML2K2 Regards

Derive an expression for the kinetic energy of a body of mass (m) rotating uniformly about a given axis. Show that the rotational kinetic energy = 1/2M (L/K)^2 Where symbols have their usual meanings.