Suppose a student wants to design an amusement park ride that moves people in a circle at uniform speed. Which concept should the student apply to ensure riders stay safely in their seats during the circular motion?

The correct option is: A constant inward (centripetal) force is needed on the riders to keep them in uniform circular motion

Step-by-step Explanation:

1. Understanding Uniform Circular Motion:
When an object moves in a circular path at a constant (uniform) speed, its direction of motion is constantly changing. Because velocity is a vector quantity (having both magnitude and direction), a change in direction means the object is continuously accelerating.

2. Role of Centripetal Acceleration and Force:
According to Newton's first law of motion, an object in motion will continue to move in a straight line at a constant speed unless acted upon by a net external force. To continuously bend the path of the riders into a circle, a force must act perpendicular to their velocity vector at every point.

This acceleration is directed toward the center of the circular path and is called centripetal acceleration ($a_c$):

$a_c=\frac{v^2}{r}$

3. Applying Newton's Second Law:
By Newton's second law ($F=ma$), the net inward force required to produce this centripetal acceleration is the centripetal force ($F_c$):

$F_c=\frac{m{v}^2}{r}$

4. Conclusion:
To keep riders safely in uniform circular motion, the ride design must ensure that a constant inward (centripetal) force is continuously exerted on them toward the center of rotation.