How to find the radius of the circle that a car will follow

In summary, the conversation discusses the process of calculating the radius of a circle that a car will follow when turning its wheels at a given angle to its current velocity. The conversation provides hints and advice on how to approach and solve this problem, emphasizing the importance of deriving equations rather than relying on existing ones.
  • #1
dpapadim
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TL;DR Summary
I was wondering how one can calculate the radius of the circle a car will follow if it turns its wheels a given angle to its current velocity?
I was wondering how one can calculate the radius of the circle a car will follow if it turns its wheels a given angle to its current velocity? For example, if i turn the wheels of my car by 12 degrees to my current direction, how large of a circle will the car perform
 
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  • #2
When confronted by a problem like this, it helps to look at if from different directions. Keep trying until you find a direction that allows you to derive the equation(s). Expect that you will have to derive the equation(s), rather than finding "the" equation(s) in a book or online.

Hint 1: The front and rear tires are tangent to the circle.

Hint 2: The inside front tire and inside rear tire are tangent to the same circle. The outside tires are tangent to a different circle.

Hint 3: Lay it out in a sketch and the math will follow.

Hint 4: The two front tires are turned to different angles because they roll on different circles.
 

1. What is the formula for finding the radius of the circle a car will follow?

The formula for finding the radius of the circle that a car will follow is r = v^2/a, where r is the radius, v is the speed of the car, and a is the centripetal acceleration.

2. How do you determine the speed of the car in the formula?

The speed of the car can be determined by using a speedometer or by measuring the distance traveled and the time taken. The speed should be in meters per second (m/s) for the formula to work.

3. What is centripetal acceleration and how is it calculated?

Centripetal acceleration is the acceleration that a body experiences when moving in a circular path. It is calculated by dividing the square of the velocity by the radius of the circle.

4. Can the radius of the circle a car will follow change?

Yes, the radius of the circle a car will follow can change depending on the speed of the car and the centripetal acceleration. A higher speed or a higher centripetal acceleration will result in a larger radius, while a lower speed or a lower centripetal acceleration will result in a smaller radius.

5. How does the radius of the circle a car will follow affect its turning ability?

The radius of the circle a car will follow directly affects its turning ability. A smaller radius means the car will be able to make tighter turns, while a larger radius means the car will require more space to turn. This is why cars with a smaller turning radius are more maneuverable in tight spaces.

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