Amerry-go-round has a radius of 2.6 m and a moment of inertia 857 kg · m2. a boy of mass 44 kg runs tangent to the rim at a speed of 5.0 m/s and jumps on. if the merry-go-round is initially at rest, what is the angular velocity (in rad/s) after the boy jumps on? (enter the magnitude.)

To give an appropriate solution to this problem we require the concepts of Angular Moment and Inertia Moment,

The angular velocity is given by,

Where,

L is the initial angular momentum, equal to

And I the moment of inertia, which for a point rotating in a circle is given by

Here m is the mass and r the radius.

For our problem the values are,

Then the angular momentum is

In the other hand the moment of inertia of the system is,

Finally we can calculate the angular momentum, which is given by,

Therefore the angular velocity after the boy jumps on is 0.584rad/s

this is poiselle's equation from fluid mechanic in physics. mech eng