- #1

RoyalCat

- 671

- 2

Well, I've recently been introduced to the wonderful world of angular momentum and precession motion, and a question popped into mind.

Why, exactly, does a wheel rolling across the ground, not topple over even if tipped to one side?

I've tried approaching the problem by looking at the angular momentum vector and looking at what torque is acting to change it, but I haven't had much luck in the matter. Maybe if I could draw in 3D I'd succeed.

An approach involving measuring the torque about the center of mass proved quite fruitless, since gravity doesn't have a torque about the center of mass. I tried finding the torque applied by the static friction, but that didn't get me anywhere (Isn't the static friction just 0 for rolling motion?)

Trying to measure the torque about the point of contact got me a bit more ahead, but nothing came to fruition.

If I tilt the wheel by an angle [tex]\theta[/tex] on its side, in the direction of its angular momentum vector, then gravity applies a torque relative to the point of contact with the ground of [tex]mgR\sin{\theta}[/tex]

The direction of this vector is perpendicular to the angular momentum, but I'm having trouble seeing how it contributes to stabilizing the wheel, if my analysis is at all correct.

I've tried running a google search for it, but that didn't help out either.

If someone could point me to a link, or explain it himself, I'd be very appreciative. :)

I think I've hit upon something.

Analyzing what happens when an external force is applied to the stable rolling wheel shows that there is a torque vector about the center of mass preventing the change in the direction of the angular momentum by the toppling over the point of contact?

Heh, that made a lot more sense in my head. Assistance is still needed. ^^;

Why, exactly, does a wheel rolling across the ground, not topple over even if tipped to one side?

I've tried approaching the problem by looking at the angular momentum vector and looking at what torque is acting to change it, but I haven't had much luck in the matter. Maybe if I could draw in 3D I'd succeed.

An approach involving measuring the torque about the center of mass proved quite fruitless, since gravity doesn't have a torque about the center of mass. I tried finding the torque applied by the static friction, but that didn't get me anywhere (Isn't the static friction just 0 for rolling motion?)

Trying to measure the torque about the point of contact got me a bit more ahead, but nothing came to fruition.

If I tilt the wheel by an angle [tex]\theta[/tex] on its side, in the direction of its angular momentum vector, then gravity applies a torque relative to the point of contact with the ground of [tex]mgR\sin{\theta}[/tex]

The direction of this vector is perpendicular to the angular momentum, but I'm having trouble seeing how it contributes to stabilizing the wheel, if my analysis is at all correct.

I've tried running a google search for it, but that didn't help out either.

If someone could point me to a link, or explain it himself, I'd be very appreciative. :)

**EDIT:**I think I've hit upon something.

Analyzing what happens when an external force is applied to the stable rolling wheel shows that there is a torque vector about the center of mass preventing the change in the direction of the angular momentum by the toppling over the point of contact?

Heh, that made a lot more sense in my head. Assistance is still needed. ^^;

Last edited: