A solid sphere rolls without slipping on a horizontal plane. The ratio of translational kinetic energy to rotational kinetic energy is:
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A solid sphere rolls without slipping on a horizontal plane. The ratio of translational kinetic energy to rotational kinetic energy is:

G1 Physics · Accepted Answer

K t r a n s = ( 1 / 2 ) m v 2 . K_trans=(1/2)mv². K t ​ r an s = ( 1/2 ) m v 2 . For a solid sphere I=(2/5)mR² and v=ωR, so K r o t = ( 1 / 2 ) I ω 2 = ( 1 / 5 ) m v 2 . K_rot=(1/2)Iω²=(1/5)mv². K r ​ o t = ( 1/2 ) I ω 2 = ( 1/5 ) m v 2 . Therefore K t r a n s / K r o t = ( 1 / 2 ) / ( 1 / 5 ) = 5 / 2. K_trans/K_rot=(1/2)/(1/5)=5/2. K t ​ r an s / K r ​ o t = ( 1/2 ) / ( 1/5 ) = 5/2.