A phonograph record of radius 6 cm and mass 15 g is rotating with an angular velocity of 33.33 rev/min. A Penny of mass 1 g suddenly falls on the record and lands at the radial distance of 4 cm from the record’s center. What is the angular velocity after the collision.

Answer 1

The turntable will not slow down if the power is on. A motor keeps it moving at 33.33 rpm. Records (LP) did not have 6 cm radius; it was 6 inches.

If the record player were "coasting" and under no power, you would still need to know the mass of the turntable platen under the record, if you want to predict final angular velocity.

They may want to to apply conservation of angular momentum, but this is a poor choice of problem for applying it.