Now, consider an example of a person riding a roller coaster through a circular section of the track, a "looptheloop."
Let's look at the formulas needed to calculate the normal force, N, exerted on a object traveling on the inside surface of a vertical circle as it passes through the bottom and through the top of the ride.
At the top:
net force to the center = N + mg N + mg = m(v^{2}/r) N = m(v^{2}/r)  mg
While at the bottom:
net force to the center = N  mg N  mg = m(v^{2}/r) N = m(v^{2}/r) + mg If we let the value of normal approach zero in the formula for the top of the roller coaster we would get the same value for the critical velocity that we got when solving for the tension in the string in our previous discussion, v = √(rg). This principle of critical velocity is used in many places. When you watch clothes drying in a dryer, they are being rotated in a vertical circle. But the rate of rotation does not allow the clothes to achieve this critical value as they pass through the top of the circle. Therefore the clothes fall away from the drum and are "fluffed" as they spin. In roller coasters, this critical velocity is a safety threshold. The coasters MUST exceed this minimum value in order to be certified. Obviously, no one would want the cars to fall away from the rails as the participants experience a thrill passing through a "looptheloop" section of the track! The value of the normal at the bottom of the ride is equivalent to questions asking about the apparent weight of a pilot as he pulls out of a vertical drive. The expression a = v^{2}/r + g is often called the "g's" a pilot is experiencing.
Note that the normal, N, appears to play the same role as the tension, T, in our equations for vertical circular motion.
