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3 years ago

12

The rotational inertia of a collapsing spinning star changes to 2/5 its initial value. what is the ratio of the new rotational k

inetic energy to the initial rotational kinetic energy (kenew / kei)?

1 answer:

Alexandra [31]3 years ago

4 0

Let K.E $_{i}$ be the intial K.E and K.E $_{new}$ be new K.E,

I $_{new}$ = $\frac{2}{5} I _{i}$

K.E $_{i} = \frac{I_{i} w^{2} }{2}$ --- (i)
K.E $_{new} = \frac{I_{new}w^{2} }{2}$

Therefore,
K.E $_{new} = \frac{2I_{i}w^{2} }{5*2}$ ----(ii)

Dividing i and ii,

$\frac{K.E_{new} }{K.E_{i} } = \frac{2}{5}$

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We also know that the asteroids are identical so their masses are identical:

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This is going to be helpful because the volume of a sphere is:

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And know we can write our original force of gravity equation in terms of the radius of the asteroids:

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