a) TO solve the problem we need to apply the conservation of angular momentum,

where,
I is the moment of inertia for the turntable, which is
m= the mass of the beetle
M= mass of the turntable
clearing
,

We know that
. So,
Making a reference and asking where is the beetle we can see that it is on the turntale.
Therefore

b) As we have seen in part a, it is

c) The angular velocity of the beetle is RELATIVE TO THE TURNTABLE, That is
