The Final angular velocity of the sphere is : Half of its initial value ( W/2 )
Given that The kinetic energy of a rotating body ( K ) = 1/2 IW² --- ( 1 )
where : I = moment of inertia, w = angular velocity
I = [tex]\frac{2}{5} MR^{2}[/tex]
Therefore equation ( 1 ) becomes
K = [tex]\frac{1}{5}MR^2W^2[/tex] ----- ( 2 )
After doubling the radius
R' = 2R
K' = K
Mass = unchanged
therefore :
[tex]\frac{1}{5}MR'^2W'^2 = \frac{1}{5}MR^2W^2[/tex]
= ( 2R )² W'² = R²W²
Resolving equation above
Hence : W' ( new angular velocity ) = W / 2
In conclusion The Final angular velocity of the sphere is : Half of its initial value ( W / 2).
Learn more about Kinetic energy of a rotating body :https://brainly.com/question/25959744
