Answer to Question #153417 in Classical Mechanics for Rokas

Question

How should I calculate the angle by which two wheels are rotated driving the vehicle around the circle. I do know circle radius, wheel radius, car length and distance between wheels. Thanks

Answer 1

$\text{the car moves in a circle, therefore all points of the car move in}$

$\text{circles with one common center}$

$\text{let } r -\text {wheel radius}$

$R -\text{radius of the circle of movement}$

$l - \text{car length}$

$w -\text{car width}$

$\text{also assume that the rear wheels of the car}$

$\text{do not turn}$

$\alpha_1,\alpha_2 \text{ angles of inclination of the front wheels}$

$L - \text{distance between axles car}$

$L= l-2r$

$\sin(\alpha_1)= \frac{L}{R}=\frac{l-2r}{R}$

$\sin(\alpha_2)= \frac{L}{R-w}=\frac{l-2r}{R-w}$

$\text{we assume that the radius of the circle of movement }$

$\text{is much greater than the width of the car}$

Answer: $sin(\alpha)=\frac{l-2r}{R}$