# How to find radius if I know angle and velocity

1. Sep 22, 2009

### chiarama

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.

2. Sep 22, 2009

### Gear300

Radius of the arc of the turn or radius of the wheel?

3. Sep 22, 2009

### chiarama

radius of the arc of the turn. Thank you for interest!

4. Sep 22, 2009

### Gear300

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. Sep 23, 2009

### chiarama

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. Sep 23, 2009

### Gear300

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. Sep 24, 2009