How to find radius if I know angle and velocity

In summary, the speaker is designing an RC car and needs to calculate the radius of the arc of a turn. They mention that the angle of the wheel and car velocity are known, and they believe they learned how to calculate the radius in a general physics class. However, they do not remember the exact equation. The speaker shares their own calculation, which involves the angle of the wheel, the length of the car, and the tangential velocity. They also mention that their answer may not be correct and ask for confirmation or correction. Another speaker also shares their own calculation and questions the relationship between the length of the car and the radius. The conversation ends with confusion about the dimensions and the comparison between a car and a bus.
  • #1
chiarama
4
0
I'm designing RC car and need to know the radius of circle when I drive corner.
I know the angle of the wheel and car velocity.

how can I calculate? I think I learned about it in the general physics class but I don't remember.
 
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  • #2
Radius of the arc of the turn or radius of the wheel?
 
  • #3
Gear300 said:
Radius of the arc of the turn or radius of the wheel?

radius of the arc of the turn. Thank you for interest!
 
  • #4
When you said angle of wheel, I'm assuming the angle of the front wheel is turned in order for turning the car.

I made assumptions here and there, and so according to experience, there is a good chance I made some mistakes. According to what I got, the velocity does not determine the radius of the curve, but the angle of the wheel, thetaw, and the length of the car, le, do (so you'll need an additional measurement). Also, the translational velocity of the wheels is not the translational velocity of the car while turning - I got v*cos(thetaw) for that value (disregarding friction while turning). What I got for the radius was r = 1/(le*tan(thetaw)). If anyone could confirm/correct it, it'd be helpful.
 
  • #5
Gear300 said:
When you said angle of wheel, I'm assuming the angle of the front wheel is turned in order for turning the car.

I made assumptions here and there, and so according to experience, there is a good chance I made some mistakes. According to what I got, the velocity does not determine the radius of the curve, but the angle of the wheel, thetaw, and the length of the car, le, do (so you'll need an additional measurement). Also, the translational velocity of the wheels is not the translational velocity of the car while turning - I got v*cos(thetaw) for that value (disregarding friction while turning). What I got for the radius was r = 1/(le*tan(thetaw)). If anyone could confirm/correct it, it'd be helpful.

I tried to prove your answer but I couldn't. can you explain how you got that result?
And when you mention the length of the car, do you mean distance between center of front and rear wheel?
 
  • #6
chiarama said:
And when you mention the length of the car, do you mean distance between center of front and rear wheel?
Yup.

The car movement could be modeled as an arc of a circle. With a constant speed the centripetal acceleration is a = v2/r. Usually when referring to cars in circular motion, it is said that the static friction provides the centripetal force (otherwise there will be kinetic friction and the car speeds in a tangent). However, the car does not have to be in circular motion to experience static friction, so more directly or indirectly, what is allowing for the the motion is the turn/angle of the wheel. What I did was I first just focused on the car as my system (you can draw it out as a line that is moving forward with a velocity v, in which the length of the line is the length of from the rear wheel to the front wheel). In this situation, the only wheels turned are the front wheels; therefore, the velocity at the front of the car/line is at an angle to the car/line, so part of the velocity is in the forward direction of the car and part is in the perpendicular direction. Since the rear wheels are focused on the ground by static friction, you could look at it as the line moving forward with a velocity equivalent to the component in the forward direction (v*cos(thetaw)) and rotating due to the component perpendicular to the car (v*sin(thetaw)). As the line rotates, the forward direction changes - altogether, you have the car moving in an arc. The angular velocity of the rotation of the car is negative the angular velocity of the revolution of the car. The centripetal acceleration is also a = v*w (w is the angular velocity of the revolution and v is the tangential velocity, which is v*cos(thetaw )). With that, you can solve for the radius. Of course, I might also be wrong about this.
 
  • #7
chiarama said:
I tried to prove your answer but I couldn't. can you explain how you got that result?
And when you mention the length of the car, do you mean distance between center of front and rear wheel?

Gear300 said:
When you said angle of wheel, I'm assuming the angle of the front wheel is turned in order for turning the car.

Also, the translational velocity of the wheels is not the translational velocity of the car while turning - I got v*cos(thetaw) for that value (disregarding friction while turning). What I got for the radius was r = 1/(le*tan(thetaw)). If anyone could confirm/correct it, it'd be helpful.

Thank you for your answer!
I also tried to solve this problem in my way and got different result with yours. in case of my result, length of the car is proportional to the radius.
when we think about bus and car, which one has smaller radius when turn? its confusing..lol

and when we think about the dimension, if we have 1/le in the result, it will be 1/m which is incorrect...
 
Last edited:

1. What is the formula for finding the radius if I know the angle and velocity?

The formula for finding the radius if you know the angle and velocity is r = v^2 / g * sin(2θ), where r is the radius, v is the velocity, g is the acceleration due to gravity, and θ is the angle.

2. Can this formula be used for any angle and velocity?

Yes, this formula can be used for any angle and velocity. However, it assumes that the object is being launched from the ground and there is no air resistance.

3. How do I determine the angle and velocity in order to find the radius?

The angle and velocity can be determined by conducting an experiment or using a simulation. You can also use mathematical equations to calculate them based on other known variables such as distance, time, and height.

4. Is there only one possible radius for a given angle and velocity?

No, there are multiple possible radii for a given angle and velocity. This is because the radius is influenced by other factors such as air resistance, launch height, and launch location.

5. Can this formula be used for any type of object or only for objects launched from the ground?

This formula is specifically designed for objects launched from the ground. For other types of objects, such as those launched from a height or moving horizontally, a different formula would be needed to calculate the radius.

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