With a small radius of curvature at the top, the centripetal acceleration can more easily be kept greater than g so that the passengers do not lose contact with their seats nor do they need seat belts to keep them in place. A circular loop would cause a jolting change in acceleration at entry, a disadvantage discovered long ago in railroad curve design. The circumference of the circle will be equivalent to pi () multiplied by the radius R. The speed and angular speed of the object are not constant. The object’s velocity vector is always tangent to the circle. In particular, the following will be true. This means that the centripetal acceleration builds from zero to a maximum at the top and gradually decreases again. In non-uniform circular motion, an object’s motion is along a circle, but the object’s speed is not constant. Teardrop-shaped loops are used in the latest roller coasters so that the radius of curvature gradually decreases to a minimum at the top. What is the speed of the roller coaster at the top of the loop if the radius of curvature there is 15.0 m and the downward acceleration of the car is 1.50 g? Figure 11. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. This allows the total force exerted on the rider by the cage to be along its axis at all times.ĩ: Modern roller coasters have vertical loops like the one shown in Figure 11. (credit: NASA) (b) Rider in cage showing how the cage pivots outward during rotation. (a) NASA centrifuge used to subject trainees to accelerations similar to those experienced in rocket launches and reentries.
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