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Recently I wondered why rotating a wheel, like on a bicycle for example, results in changing the direction of its velocity. Hence I read about the Ackermann steering geometry and watched various videos on the steering mechanisms of cars. However, none of these sources could clarify my current misconception, namely, is the kinetic frictional force the cause of the turning of the wheel? Moreover, I conceived a possible explanation for why it must be the kinetic frictional force, which is graphically shown in the image below. enter image description here

In situation A, where the force required to turn the wheel is considered negligible, the entire wheel has a translational velocity $\vec{v_{T}}$ and rotational velocity $\vec{v_R}$. Since $\vec{v_{T}}$ and $\vec{v_{R}}$ aren't parallel, there is relative motion between the wheel and ground, therefore a kinetic frictional force must occur as long as sliding persists. Furthermore, $\vec{f_\parallel}$ will cause $\vec{v_R}$ to increase and $\vec{v_\parallel}$ to decrease, until both vectors are equal in size and opposite in direction. Then the relative motion of the wheel to the ground will be 0 in the direction of $\vec{v}$ (situation B), and $\vec{f_\parallel}$ becomes 0 as well. Now the only relative motion that remains is due to $\vec{v_\perp}$ and this component of $\vec{v_T}$ must become 0 in order for it to point in the direction of $\vec{v}$. This could solely be accomplished via $\vec{f_\perp}$, which will eliminate $\vec{v_\perp}$ due to the sliding motion. Eventually the wheel is going to end up in situation B, as was to be demonstrated.

I would be grateful if you could tell me if this given explanation is correct.

P.S. In this analysis, I ignored the fact that the wheel would tip over during the sliding because of an upward torque caused by the kinetic frictional force.

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  • $\begingroup$ "is the kinetic frictional force the cause of the turning of the wheel?" Kinetic friction doesn't cause anything to move (rotate or translate). Static friction does. $\endgroup$
    – Bob D
    Jul 4, 2021 at 16:30
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    $\begingroup$ Spinning wheels on a drag racer can produce kinetic friction which accelerates the car. Locking the brakes on a car can put it into a skid during which kinetic friction brings it to a stop. $\endgroup$
    – R.W. Bird
    Jul 4, 2021 at 20:23

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On my bicycle increasing or decreasing speed does not change the direction of the angular velocity vector of the wheels. If I want to change direction, I apply a torque with the handlebars. When riding without hands, a slight tip to the right produces a torque (which does require static friction with the road). That torque causes the front wheel to precess to the right, which shifts the center of support to the right. Bottom line: I don't understand your question.

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