Body describes a closed trajecty on a free-to-spin disk

[Gena]

[Moderator's Note: Thread title changed to better reflect the problem statement]

Homework Statement

A body of mass m is on a disk of mass M=2m and radius R, initially static and free to spin around its center. The mass mm goes around a trajectory described in the image below with constant velocity v with respect to the platform. The circular arcs of the trajectory have a radium of R/4 and 3R/4 and an aperture of 90 degrees with respect to the disk.

After completing the trajectory, the mass stops.
What angle does the disk spin with respect to its original position?

Homework Equations

Probably something related to conservation of the angular momentum or something, but honestly could be anything.
L=Iw
P=mv

The Attempt at a Solution

no clue whatsoever on how to even approach this problem, any hint will be happily received. Thanks

 

[haruspex]

Probably something related to conservation of the angular momentum

Right. So consider each of the four movements in turn. What equations can you write for angular belocities and displacements?

constant velocity

Well, constant speed.

 

[scottdave]

What do you think the disc will be doing when the particle makes the turn and is moving toward (or away from) the center? Do you know what I is for the disc and for the particle?