Here are the essential concepts you must grasp in order to answer the question correctly.
Centripetal Force
Centripetal force is the net force acting on an object moving in a circular path, directed towards the center of the circle. In the context of the amusement park ride, this force is necessary to keep the riders moving in a circular motion. It is provided by the gravitational force acting on the riders and the normal force from the ride's structure.
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Gravitational Force
Gravitational force is the attractive force between two masses, which in this case is the force acting on the riders due to Earth's gravity. At the top of the ride, this force must be sufficient to provide the necessary centripetal force to keep the riders from falling off. The gravitational force can be calculated using the equation F = mg, where m is the mass and g is the acceleration due to gravity.
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Period of Rotation
The period of rotation is the time it takes for one complete revolution around a circular path. It is related to the angular velocity and the radius of the circular motion. In this scenario, the longest rotation period corresponds to the slowest speed at which the ride can operate while still providing enough centripetal force to keep the riders safely in place at the top of the loop.
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