An ice skater starts a spin with her arms stretched out to the sides. she balances on the tip of one skate to turn without friction. she then pulls her arms in so that her moment of inertia decreases by a factor of two. in the process of her doing so, what happens to her kinetic energy?

I₁ = initial moment of inertia before pulling in the arms

I₂ = final moment of inertia after pulling in the arms = I₁ /2

w₁ = initial angular velocity before pulling in the arms

w₂ = final angular velocity after pulling in the arms

using conservation of angular momentum

I₁ w₁ = I₂ w₂

I₁ w₁ = (I₁/2 ) w₂

w₂ = 2 w₁

KE₁ = initial rotational kinetic energy before pulling in the arms = (0.5) I₁ w²₁

KE₂ = final rotational kinetic energy after pulling in the arms = (0.5) I₂ w²₂

Ratio of final rotational kinetic energy to initial rotational kinetic energy is given as

KE₂ /KE₁ = (0.5) I₂ w²₂/((0.5) I₁ w²₁ )

KE₂ /KE₁ = ((I₁/2 ) (2 w₁)²)/(I₁ w²₁)

KE₂ /KE₁ = 2

KE₂ = 2 KE₁

hence the kinetic energy becomes twice

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .