Circular motion: static or dynamic friction?

[tiny-tim]

A simple question, but I can't find the answer anywhere …

when something (otherwise unconstrained) is pulled by rope (approximately forwards) so as to slide (not roll) at constant speed in a circle on a rough surface, the total acceleration is obviously centripetal (radial)

there are two forces, one is along the rope, and the other is friction

is the friction force entirely dynamic, so that it is calculated as the normal force times the coefficient of dynamic friction?

or is it calculated as partly times the dynamic coefficient in the forward direction (the direction of actual relative motion between the surfaces), and partly times the static coefficient in the radial direction (as it would be in the purely rolling case)?

I've always assumed it's entirely dynamic, but that seems a little illogical.

Anyway, this is an experimental question rather than a theoretical one, so does anyone know of any experiments on the subject?

 

[rcgldr]

The total acceleration would not be centripetal. Although the path remains a circle, you'd have the velocity changing directions to follow the circular path, but at the same time a reduction in the magnitude of the velocity. So there would be both a centripetal acceleration and a tangental deceleration.

 

[BradP]

Hm? He said speed was constant, so the magnitude of the velocity is constant. Thus the only acceleration would be in the radial direction.

I think friction force would be entirely in the (opposite) direction of motion. Centripetal force is m*(v^2)/r. As long as it continues in a circular path at constant velocity, the radial force must be constant. If friction force acted in a direction other than that of motion, it would knock it off of the circular path. That is my reasoning.

 

[rcgldr]

when something (otherwise unconstrained) is pulled by rope (approximately forwards) so as to slide (not roll) at constant speed in a circle on a rough surface, the total acceleration is obviously centripetal (radial).

I missed the part about constant speed. The acceleration is centripetal, but the force would involve a tangental component equal to and opposing the kinetic friction. The rope's direction would line up with the force, and be oriented "ahead" of the center of the circle. Assuming a fixed length rope, then the inside end of the rope would also travel in a circular path, with a smaller radius than the object being pulled. This could be done by attaching the rope to the edge of a rotating disc.

 

[K^2]

As long as you have relative motion of surfaces in any direction, friction is entirely kinetic.

That's why you don't want your tires to skid while making a turn. Even though hitting the brakes causes tires to begin sliding on surface in direction of motion (tangential), the fact that you are now in kinetic friction mode means that you just lost a big chunk of your centripetal force, and can no longer make the curve.