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### Course: Physics library>Unit 4

Lesson 1: Circular motion and centripetal acceleration

# Optimal turns at Indianapolis Motor Speedway with JR Hildebrand

Created by Sal Khan.

## Want to join the conversation?

• Fascinating discussion! I'm curious what the relative radii of these three circles around the track are.
• The increased radius of the much larger circle really opened my eyes to the problem. Its like the driver is performing the best "trade-off" or "compromise" between centripetal force and the work required to complete the turn AS WELL AS setting up the car to then accelerate down the straight line as quickly as possible. Another instance of mathematics underlying everything that happens, even if we are unaware of it while we do it.
• Cool! But what about if you were running, what is faster?
• I guess the Inner circle would be a better option then.
Because when running, you aren't at much velocity. So you'll not face much Centripetal Force because in the formula,
`` Centripetal Force is directly proportional to the Square of Velocity. ``

And also You can observe in Olympic and other races the players choose the Inner circle always.
• As the car rounds the turn, does it lose speed due to the extra work needed to maintain the turn including friction; and if so, though the pedal is to the metal, is the car losing speed though accelerating?
• Even at full throttle around the corner the car will lose speed due to tire drag as the inertia of the car would love to continue straight ahead, yet the input from the driver (steering wheel through to tire contact patch) is asking the car to turn. The result of these forces, if the driver is correct, will be that the car changes direction (success), but then also loses speed (a clear trade off) as the tires themselves twist and flex to balance the forces interested in continuing on said path (inertia) and the driver's interest in changing direction. The driver turns the steering wheel; this continues down through the metal steering rod, rack/pinion, and out to the steel wheels. Everything is a solid metallic connection. Then, you reach the tires. It is the tires that mediate between the massive momentum (and therefore inertia) and the driver's interest in turning. In order to make it all work, the tires must twist (slip angle) between what the driver is asking the car to do, and what the pavement and grip level of the tires will allow. I'm sure there are plenty of other discussions about slip angle; I'm not an engineer, but I am a supporter of Mr Hildebrand, whom I've known well over a decade and believe in immensely; good luck JR! -DMc.
• Can any other car take such sharp turns if they used the same tire?
(1 vote)
• No. Cornering ability is also a function of the vehicle's suspension, weight, downforce, and many other things. Also, race tires are designed to heat up at speed and become more "sticky". A regular vehicle would not drive fast enough to heat up race tires properly.
• I am a little confused weather the centripetal acceleration decreases the speed of car. Becouse in the previous videos Sal told about the constant speed the object has during circular motion.
• The centripetal acceleration does not decrease the speed of the car. The problem with having more centripetal acceleration is that you have to accelerate the car very quickly over an even shorter period of time and most cars just won't be able to make that acceleration fast enough. Hope this helps!
• Wait, so is a higher centripetal acceleation better for a race car driver?
• He needs the right amount for the speed he has and the radius of the turn he is making.
• Would the best thing to do in this situation (as the driver) be finding the smallest radius possible without going over the max centripetal force the car can handle? I don't understand why the driver would want to take the route with the largest R if they don't need to.
(1 vote)
• The objective is not to minimize distance or maximize speed of the car, it's to minimize the time it takes to complete the race. That requires some optimal combination of finding a short path while keeping as much speed as possible. If you have to slow down too much to take the smallest radius, it's better to take a bigger radius that lets you avoid slowing down. It's a lot more complicated than it looks!
• The thing thats nagging me[stupid thing really] is that why does the path he chooses matter cause if he chooses the shortest path i.e. the inner one then by mv^2/r he has more centripetal acceleration so less chances of overturning or skidding so isnt a small radius better than a larger one.
(1 vote)
• For the inner one he doesn't HAVE more centripetal acceleration he NEEDS more centripetal acceleration. Since that acceleration comes from a frictional force applied the tires, his chance of overturning or skidding is HIGHER when he tries to take the tighter turn at the same speed.
• Where does Centripetal Force of car travelling on a banked curve come from? It has Fgy and Normal Force in vertical direction, and Friction and Fgx in horizontal direction all cancelled out right?
• No. Friction + the component of the normal force that is parallel to the ground give you a net centripetal force.