Episode 6: How Roller Coasters Keep You on the Track at the Top of a Loop 🎢

Hey loyal STEMiscope blog readers! Ever been to a theme park or ride, and wondered about how rollercoasters work? Well, you're in luck-- we will be discussing this in depth in today's blog!

When you are sitting in a roller coaster going through a big loop, there is a moment when you are completely upside down. It feels like gravity disappears for a second and you are just hanging there. But of course, gravity is still there. In fact, gravity is one of the main reasons you stay safely in your seat. The real idea behind this is called centripetal force.

Centripetal force means "center seeking", and it is the force that keeps any object moving in a circle instead of flying off in a straight line. When something moves in a circle, its direction is always changing (change in velocity), which means it is always accelerating. To accelerate, there must be a force pulling the object toward the center of the circle. That is the centripetal force.

At the very top of a roller coaster loop, two forces act on you at the same time:

Gravity (mg): this force always points straight down toward the ground.

Normal force (N): this is the push from your seat or harness, and when you are upside down, it also points downward, toward the center of the loop.

At that moment, both of these forces are pointing in the same direction. Together, they provide the centripetal force needed to keep you moving in a circle. The equation for this looks like:

Here, (mv^2)/r is the centripetal force, m is your mass, v is your speed at the top of the loop, r is the radius of the loop, N is the normal force, and mg is your weight.

If the roller coaster is going very fast, the seat must push on you harder, which means the normal force is large. If it goes slower, the seat doesn’t have to push as hard, but gravity still helps a little to keep you moving along the loop. If the coaster ever went too slow, the normal force could drop to zero, meaning gravity alone provides just enough centripetal force to keep you barely in your seat. That’s why roller coasters are designed to go fast enough at the top of loops so you’re never in danger of falling.

Inertia naturally wants to make your body move in a straight line, away from the curve of the loop. But the combination of the seat pushing toward the center, gravity pulling down, and your speed around the loop provides the inward centripetal force that keeps you safely on track.

In short, moving fast enough through the loop, along with the forces acting toward the center, keeps you pressed into your seat even when you’re upside down.

You can even find the minimum speed needed to stay on the track by setting the normal force to zero in the equation:

This shows that the larger the radius of the loop, the faster the coaster has to move to keep everyone safe.

When you reach the top of the loop, both gravity and the seat’s push are pulling you toward the center, so you actually feel lighter than normal. Some people even feel almost weightless for a split second. At the bottom of the loop, the situation is the opposite. Gravity is pulling you down, but the seat is pushing you up to keep you moving in a circle, and that makes you feel heavier. That is why your stomach feels like it drops at the top and gets heavy at the bottom.

Another interesting detail is that roller coaster loops are not perfect circles. If they were, the forces at the bottom would be too strong and uncomfortable. Instead, loops are shaped like teardrops, called clothoid loops, which make the motion smoother and reduce extreme g-forces. Engineers design them so that you feel just the right amount of thrill without it being unsafe.

So when you are upside down at the top of a roller coaster, you are not defying gravity at all. Gravity and the seat’s push are both working together to pull you toward the center of the loop. That perfect balance of forces keeps you safe and makes the ride so exciting. The next time you ride a loop, try to think about the physics behind it. You will probably still scream, but at least you will know exactly why you are not falling out.