# Effects of vertical circular motion to the body weight

Our body weight will experience the differences when moving at constant speed in a vertical circular motion such as roller coaster. Why do we feel heavier when at the bottom of the loop and lighter when at the top ?

When you are at the bottom of a roller coaster about to move upwards (in say a circular motion), the net force you experience is given by,

$F_{net} = \frac{mv^2}{r}$

The forces acting on you are the normal force of the track $N$, and gravity, $mg$.

Therefore,

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

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

This normal force is the force the track is pushing up on you, and it is what makes you feel heavy.

When you are at the top of the roller coaster moving down, again assume in circular motion, the net force is now given by,

$F_{net} = -\frac{mv^2}{r}$

Now we have,

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

Thus,

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

Therefore the normal force is less at the top of the track than at the bottom.

This can be understood intuitively as when you are moving upwards, gravity is opposing the centripetal motion and thus the normal force must be greater to compensate.

When you are moving downwards in circular motion, gravity is assisting this centripetal acceleration, and thus less normal force is required from the track.