When you’re upside down at the top of a vertical looping roller coaster, why is the centripetal force acting on you the least of anywhere in the loop?
In: Physics
The centripetal force is actually constant, assuming the car is going at a constant speed, because the centripetal force equation is mv²/r – mass isn’t changing, assuming a circular loop the radius isn’t changing either, so if the car’s speed doesn’t change, the centripetal force is constant.
The reason you feel less force at the top is because the **net** force is changing, not the centripetal force. The main forces at work on the car are gravity and centripetal force. Gravity always pulls down, centripetal force always pulls towards the center of the loop. Centripetal force has to be greater than gravity in order for the loop to work.
So at any point in the loop, the net force is the difference between centripetal force and gravity. At the bottom, their signs are opposite, so instead of subtracting, you add them up. At the top, their signs are pointing the same way, so you subtract gravity from centripetal force. That’s why the net force is at its maximum at the bottom, and its minimum at the top.
The centripetal force will be minimal because the speed is minimal. You lose speed when you go up and gain speed when you go down.
What feel in turn is the centrifugal force that is the result of the centripetal force from your point of view. They are in the opposite direction.
So you feel like there is a force away from the center of the loop even if the
The centrifugal force is also on the opposite side of gravity on top and you feel is the difference between it and gravity.
When you start to turn at the bottom, gravity and the centrifugal force are in the same direction so they are added together.
So the force you feel is minimal at the top because of the lowest speed and the direction of the centrifugal force and gravity.
“Angular velocity” is how fast you’d be going if the track was straight, which basically is what tries to keep you going forward but the track is turning you.
Your “angular velocity” is the slowest at the top because that’s when it starts to pick up speed again because of gravity. So then the speed of the track trying to turn you is the least at the top, which is another way of saying your centripetal force is the least at the top.
Assuming for a perfect circular track.
Because you’re speed is the slowest at that point and the force of gravity is cancelling out one g of centrifugal/centripetal force.
But… in good rollercoaster design this doesn’t happen. Rollercoasters are rarely/never designed with constant curvature, they’re actually a teardrop shape, with more gradual slopes at the beginning and end of the loop. The varying curvature is designed to keep the centripetal forces on you approximately equal for the entire trip through the loop. Without this the g forces at the start and end would be enormous, or the rollercoaster would have difficulty in getting around the loop, neither make a good ride experience.
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