Apparent Weight in Circular Motion

Apparent weight is the normal force $N$ that a surface exerts on you. When you ride a Ferris wheel or stand in an elevator, the push you feel from the seat or floor is this normal force—and that's what your body interprets as weight.

Your true weight $W = mg$ is simply gravity pulling you downward. It never changes (so long as the gravitational field is constant). But the normal force can vary when you accelerate, making you feel heavier or lighter.

At the Bottom of a Vertical Circle

Recall from vertical circular motion that at the lowest point of a Ferris wheel, the normal force from your seat pushes upward (toward the center) while gravity pulls downward (away from the center). The key insight here is that the normal force $N$ represents your apparent weight—what you actually feel.

Applying Newton's second law in the radial direction:

$$N - mg = \frac{mv^2}{r}$$

Solving for the normal force:

$$N = mg + \frac{mv^2}{r}$$

Your apparent weight $N$ exceeds your true weight $mg$ because the seat must both support you against gravity and provide the centripetal force for circular motion.

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