Uniform Circular Motion: a concept question

[kostoglotov]

Homework Statement

A particle moving along a straight line can have nonzero acceleration even when its speed is zero (for instance, a ball in free fall at the top of its path). Can a particle moving in a circle have nonzero centripetal acceleration when its speed is zero? If so, give an example. If not, why not?

Homework Equations

The Attempt at a Solution

I think the answer is no...after all, so something to be experiencing centripetal acceleration, it needs to be moving in a circle. Everything wants to just move in straight lines, but if there's friction on tyres or tension in a string, then that becomes a centripetal force giving centripetal acceleration, but that tension or friction can't exist without motion in the first place...am I right? Wrong? What's going on here?

It's says zero speed...if you're speed is zero, then you can't have direction can you?

 

[collinsmark]

Just to check, is the problem statement written down correctly, verbatim? Something about it seems contradictory to me.

The parts that confuse me, "Can a particle moving in a circle...," and "...when its speed is zero." Is the particle moving or isn't it?

[Edit: Okay, maybe it's worded correctly. Now I'm imagining a particle attached to the end of a rod, where the other end of the rod is attached to a fixed, central point, and the rod has a nonzero angular acceleration. A pendulum is a good example.

The problem statement asks specifically about "centripetal acceleration" though, not acceleration in general. There may be more than one force acting on the object, thus different influences on its overall acceleration, but the problem statement asks about the "centripetal" acceleration specifically. Keep that in mind when you form your answer.

Another Edit: The definition of centripetal acceleration, as opposed to other types of acceleration, may come into play here.]

 

[haruspex]

I think the answer is no...after all, so something to be experiencing centripetal acceleration, it needs to be moving in a circle. Everything wants to just move in straight lines, but if there's friction on tyres or tension in a string, then that becomes a centripetal force giving centripetal acceleration, but that tension or friction can't exist without motion in the first place...am I right? Wrong? What's going on here?

It's says zero speed...if you're speed is zero, then you can't have direction can you?

You are essentially correct. (In the tyres case, I assume you mean friction other than in the direction of motion.)
Can you make this more concrete with an equation?

 

[kostoglotov]

You are essentially correct. (In the tyres case, I assume you mean friction other than in the direction of motion.)
Can you make this more concrete with an equation?

Yeah, static friction perpendicular to the direction the tyres is pointed, providing the centripetal force.

 

[insightful]

It's says zero speed...if you're speed is zero, then you can't have direction can you?

A stationary ball, the instant it is released in free-fall, has a velocity vector that is zero in magnitude, so its velocity direction is moot. However, its acceleration vector has a magnitude (g) and a direction (downward).