Question

Suppose you’re eating in yet another restaurant where the dishes are shared at the table and...

Suppose you’re eating in yet another restaurant where the dishes are shared at the table and all placed uniformly on a rotating disk-like surface. Model this surface as a thin disk of radius 48.2 cm. Someone else has spun the surface, such that it is initially at an angular speed of 0.4 rev/s. The surface and food has a combined mass of 4.3 kg. The waiter, to show off, throws a new dish of dumplings (mass 0.7 kg) onto the surface at a speed of 0.6 m/s, such that the dish lands on and sticks to the very edge of the surface moving in the same direction as the rotating food. While this is happening, you quickly calculate the final angular speed of the food so that you can predict its location at any time before others have a chance to eat the dumplings. What is this speed, in rad/s?

Could you please provide a full solution with the answer shown above?

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