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a ball rolls without slipping. the radius of gyration of the ball about an axis passing through its centre of mass is k. if radius of the ball be R then fraction of total energy associated with its rotational energy in terms of k and R is what??? i didnt understand the question so will u plzzz explain??😄

a ball rolls without slipping. the radius of gyration of the ball about an axis passing through its centre of mass is k. if radius of the ball be R then fraction of total energy associated with its rotational energy in terms of k and R is what???      
i didnt understand the question so will u plzzz explain??😄

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Moment of inertia = I= MK²

1. ball is a solid sphere
I= 2/5 MR²
 rotational KE= 1/2w²= 1/2 MK²w²

total energy= 1/2 Iw² +1/2 Mv²

rolling, without slipping
v= Rw
total energy= 1/2 Iw² +1/2 MR²v²
1/2 MK²w² + 1/2 MR²w²
w²M/2= (K² + R²)

Fraction of total Energy associated with KE
1/2MK²w² divided by w²M/2 (K²+R²) = 
K²/ (K²+ R²)

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