At the end of cylindrical rod of length l = 1 m and mass M = 1 kg rotating horizontaly along the vertical axis in its center with an angular speed  a small mouse of mass m = 0.02 kg is located Determine the angular speed 
of this double system when a mouse will move to the center of rod close to the rotating axis, taking into
account that the mouse can be treated as the material point.

w = 0.943 rad / s

Explanation:

For this problem we can use the law of conservation of angular momentum

Starting point. With the mouse in the center

            L₀ = I w₀

Where The moment of inertia (I) of a rod that rotates at one end is

         I = 1/3 M L²

Final point. When the mouse is at the end of the rod

          = I w + m L² w

As the system is formed by the rod and the mouse, the forces during the movement are internal, therefore the angular momentum is conserved

        L₀ = L_{f}

        I w₀ = (I + m L²) w

        w = I / I + m L²) w₀

We substitute the moment of inertia

        w  = 1/3 M L² / (1/3 M + m) L²    w₀

        w = 1 / 3M / (M / 3 + m) w₀

We substitute the values

      w = 1/3 / (1/3 + 0.02) w₀

      w = 0.943 w₀

To finish the calculation the initial angular velocity value is needed, if we assume that this value is w₀ = 1 rad / s

        w = 0.943 rad / s

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2

the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.