Question

You want to double the radius of a rotating solid sphere while keeping its kinetic energy constant. (The mass does not change.) To do this, the final angular velocity of the sphere must be Group of answer choices

Answer 1

The Final angular velocity of the sphere is : Half of its initial value ( W/2 )

Kinetic energy of a rotating body

Given that The kinetic energy of a rotating body ( K ) = 1/2 IW² --- ( 1 )

where : I = moment of inertia,  w = angular velocity

I = $\frac{2}{5} MR^{2}$

Therefore equation ( 1 ) becomes

K = $\frac{1}{5}MR^2W^2$   ----- ( 2 )

After doubling the radius

R' = 2R

K' = K

Mass = unchanged

therefore :

  $\frac{1}{5}MR'^2W'^2 = \frac{1}{5}MR^2W^2$

= ( 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 :brainly.com/question/25959744