# Centripetal Acceleration on a car

• Raag90
In summary, the conversation discusses the concept of traction and slip in relation to the longitudinal and lateral acceleration of each wheel. The idea of using an accelerometer at the centre of gravity of a model car is also mentioned, along with the equation for lateral acceleration and its relation to angular velocity. It is noted that the average value of ω2r for the centre of mass will be the same as that for the outside and inside tyres.
Raag90
Hey guys,

Ok so for my final year project I've researched about traction and slip, etc, and I came across the traction circle, where each tyre has a specified 'budget' of friction that should never be exceeded during cornering. Now the longitudinal acceleration exerted will be different for each wheel, but my question was does the lateral acceleration exerted by each wheel have any correlation so the acceleration experienced by the centre of gravity? I was planning on using an accelerometer at the COG of the model car I had to be able to give an indication of the traction budget for the car, until I realized that the traction must be specified at each wheel (which would be tricky to do).

Any ideas much appreciated.

Hey Raag90!
Raag90 said:
… does the lateral acceleration exerted by each wheel have any correlation so the acceleration experienced by the centre of gravity? I was planning on using an accelerometer at the COG of the model car …

If an object has instantaneous radius of curvature r, and speed v, then the https://www.physicsforums.com/library.php?do=view_item&itemid=27"(lateral acceleration) is v2/r.

We can also write this as ω2r, where ω is the angular velocity, v/r … this has the advantage that ω is the same for every part of the car (which v is not).

Obviously, the centre of the car has a smaller r than the outside tyres, and a larger r than the inside tyres, but the average value of ω2r will be the same as ω2r for the centre of mass.

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## What is centripetal acceleration on a car?

Centripetal acceleration on a car is the acceleration towards the center of a circular path that a car follows. It is caused by the centripetal force, which is directed towards the center of the circle.

## How is centripetal acceleration related to speed and radius?

Centripetal acceleration is directly proportional to the square of the car's speed and inversely proportional to the radius of the circular path. This means that as the car's speed increases, the centripetal acceleration increases, and as the radius of the path increases, the centripetal acceleration decreases.

## What is the role of friction in centripetal acceleration on a car?

Friction between the car's tires and the road is responsible for providing the necessary centripetal force to keep the car moving in a circular path. This force must be equal to the centripetal force in order to maintain a constant speed and radius.

## Can centripetal acceleration cause a car to lose control?

Yes, if the centripetal force is not sufficient to overcome the car's inertia, the car can lose control and slide out of the circular path. This is known as oversteering or understeering, depending on the direction of the force relative to the car's motion.

## How can centripetal acceleration be calculated on a car?

The centripetal acceleration on a car can be calculated using the equation a = v^2/r, where "a" is the centripetal acceleration, "v" is the car's speed, and "r" is the radius of the circular path. This equation can also be rearranged to solve for the car's speed or radius, depending on the given information.

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