The disk on the bottom has a rotational inertia of i0 and is spinning clockwise on a horizontal surface having negligible friction at an angular speed of 3ω0. the top disk is then dropped directly on top of the bottom disk. the top disk has a rotational inertia of i0 and was initially spinning counterclockwise at an angular speed of ω0. if the initial total kinetic energy of the two-disk system was e0, what will the kinetic energy of the system be once the objects reach a common angular speed?

  K = I₀ w₀²

Explanation:

This is a problem of conservation of angular momentum,

We take the counterclockwise turn as positive

Initial. Before the crash

       L₀ = -I₀ 3w₀ + I₀ w₀

Final. The two albums together

       = (I₀ + I₀) wf

The moment is preserved

      L₀ =  

      -I₀ 2w₀ = (2I₀)  

         = -w₀

Let's look for kinetic energy

       K = ½ I w²

initial

       K₀ = ½ I₀ (-3w₀)² + ½ I₀ w₀²

       K₀ = ½ I₀ w₀² (9-1)

       K₀ = 4 I₀ w₀² = E₀

Final

        K = ½ 2 I₀ (-w₀)²

         K = I₀ w₀²

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

-the first industrial use of geothermal energy began near pisa, italy in late 18th century

-in 1904, italian scientist piero ginori conti invented the first geothermal electric power plant in which steam was used to generate the power

-with the above experiment, the first geothermal plant in usa started in 1922 with a capacity of 250 kilowatts

-however, in 1946 first ground-source geothermal heat pump installed at commonwealth building in portland, oregon

-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

-as effect of climate change started showing results, governments of various countries joined hands to fight against it, for which kyoto protocol was signed in japan in 1997, laid out emission targets for rich countries and required that they transfer funds and technology to developing countries, 184 countries have ratified it

hope this