Question

the translation kinetic energy of rolling body is E then the total kinetic energy of the body is​

Answer 1

Answer:

Let M and R be the mass and radius of the body, V is the translation speed, to is the angular speed and I is the moment of inertia of the body about an axis passing through the center of mass. 

Kinetic energy of rotation, ER=21MV2

 Kinetic energy of translation, Er=21Iω2

E=ER+Er

=21MV2+21Iω2

21MV2+21MK2ω2 (I=MK2 and K is the radius of gyration)

=21MR2ω2+21MK2ω2  (∵V=Rωω)

∴E=21Mω2(R2+K2)

∴E=2