Final Answer:
1) The penny closer to the center of the turntable will have a greater velocity due to the conservation of angular momentum.
This is because as the radius decreases, the velocity must increase to maintain constant angular momentum.
Step-by-step explanation:
When considering two pennies on a turntable with the same mass and experiencing the same centripetal force, the penny closer to the center of the turntable will have a greater velocity. This phenomenon can be explained by the conservation of angular momentum.
Angular momentum (L) is the product of an object's mass (m), velocity (v), and radius (r). According to the conservation of angular momentum, the total angular momentum of a system remains constant unless acted upon by an external torque. In the case of the turntable, as the radius decreases (moving closer to the center), the velocity must increase to maintain the constant angular momentum.
Mathematically, this relationship is expressed as L = mvr, where L is angular momentum, m is mass, v is velocity, and r is radius. If the centripetal force remains constant for both pennies, the one closer to the center (with a smaller radius) will experience a greater increase in velocity, while the one farther from the center will have a lower velocity.