angular velocity of a system question?

Question

A runner of mass m runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude v. The turntable is rotating in the opposite direction with an angular velocity of magnitude omega relative to the earth. The radius of the turntable is r, and its moment of inertia about the axis of rotation is I.

Find the final angular velocity of the system if the runner comes to rest relative to the turntable. (You can treat the runner as a particle.)

Thanks for any help!

Answer 1

the the ω and v are related

ω1*r=v ==> ω1=v/r
the momentum before the runners stops is

ω1*I
when the runner stops he becomes part of the disk and the momentum is
ω2*(I+mr^2). These must be conserved so

ω1*I=ω2*(I+mr^2)

solve for ω2=ω1*I/(I+mr^2)

Answer 2

L = I? ==> ? = L / I there is not any exterior rigidity performing, the rotational momentum L of the gadget disc+computer virus remains consistent. the 2nd of inertia I incorporates the 2nd of inertia of the disc, it is persevering with, and the 2nd of inertia of the computer virus, which decreases with the aid of fact the computer virus strikes from the rim to the middle of the disc. subsequently the angular velocity will advance. As for the kinetic capability, there is not any replace, with the aid of fact there is not any artwork carried out by skill of exterior rigidity.