A hollow ball rolls along the floor with aconstant linear speed v . (a) Find the

Question

A hollow ball rolls along the floor with aconstant linear speed v. (a) Find the fraction of its total kineticenergy that is in the form of rotational kinetic energy about thecenter of the ball.
Krot/Ktotal =

(b) If the linear speed of the ball is decreased to 1/2v, does youranswer to part (a) increase, decrease, or stay the same? increase
decrease
stay thesame (a) Find the fraction of its total kineticenergy that is in the form of rotational kinetic energy about thecenter of the ball.
Krot/Ktotal =

(b) If the linear speed of the ball is decreased to 1/2v, does youranswer to part (a) increase, decrease, or stay the same? increase
decrease
stay thesame increase
decrease
stay thesame increase
decrease
stay thesame

Explanation / Answer

Rotational kinetic energy K rot = ( 1/2) I 2 where I = moment of inertia = ( 2/ 3) M R2            = angular speed = v / R So, K rot = ( 1/ 3 ) M v 2 translational kinetic energy K tra = ( 1/ 2)M v 2 So, K rot / K total =[  ( 1/ 2) I 2] / [K rot +K tra  ]                               =   [ (1/ 3 ) M v 2]    / [ ( 1/ 3 ) M v2 + ( 1/ 2) M v 2 ]                              = 0.4

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