Final answer:
The ladybug's friend at the outer edge of the turntable has the same rotational speed of 20 RPM but a tangential speed of 4 cm/s, which is double the ladybug's because tangential speed is proportional to the radius.
Step-by-step explanation:
The question concerns rotational motion and tangential speed in a circular system. Given that the ladybug is halfway between the rotational axis and the outer edge of the turntable, her friend who sits at the outer edge will have a rotational speed that's the same—20 revolutions per minute (RPM). However, the friend's tangential speed will be double the ladybug's because tangential speed at the edge of a rotating object is proportional to the radius. The ladybug, being halfway, only experiences half the tangential speed compared to the edge.
Since the ladybug has a tangential speed of 2 cm/s, the friend's tangential speed at the outer edge would be 4 cm/s. This accounts for the doubling due to being at twice the distance (full radius) from the center compared to the ladybug.