why does a coasting rotating system slows down when a slice of bread is put on it?

conservation of momentum.

Angular momentum before bread = MR (mass by rotational velocity

Angular momentum after bread = (M +m)r

Neglecting frictional losses MR = (M +r)r

Since M + r > M. it follows that r < R

since kinetic energy has to be constant/or decrease and the moment of inertia has increased so the angular velocity has to decrease.../

T = 1/2 I w^2,

if I increases w has to decrease...