A uniform 2.00-kg circular disk of radius 20.0 cm is rotating clockwise about an axis through its center with an angular speed 30.0 revolutions per second. A second uniform 1.50-kg circular disk of radius 15.0 cm that is not rotating is dropped onto the first disk so that the axis of rotation of the first disk passes through the center of the second disk. What is the final angular speed of the two disks when they are rotating together

   w = 132.57 rad / s

Explanation:

To solve this exercise we must define a system formed by the two discs, therefore the angular momentum is conserved

initial

         L₀ = I₀ w₀

final

         L_f = I w

how the moment is preserved

         L₀ = L_f

         I₀ w₀ = I w

the moment of inertia of disk 1 is

         I₀ = ½ m₁ r₁²

The moment of inertia of the set is

        I = I₀ + I₂

        I = ½ m₁ r₁² + ½ m₂ r₂²

we substitute

       ½ m₁ r₁² w₀ = (½ m₁ r₁² + ½ m₂ r₂²) w

       w =

let's reduce the magnitudes to the SI system

        w₀ = 30.0 rev / s (2π rad / 1 rev) = 188.5 rad / s

let's calculate

        w = ( ) 188.5

        w = (  ) 188.5

        w = 132.57 rad / s

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

that tool is called an altimeter which measures your altitude which can be used to tell which atmosphere you are currently in, including the stratosphere.

hope this ! : )