Uniform Circular Motion: a concept question

In summary, a particle moving in a circle can have nonzero centripetal acceleration even when its speed is zero. This can occur due to external forces such as friction or tension, which provide the necessary centripetal force. The definition of centripetal acceleration, as opposed to other types of acceleration, may also come into play. A concrete example can be seen in a pendulum.
  • #1
kostoglotov
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6

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?
 
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  • #2
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.]
 
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  • #3
kostoglotov said:
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?
 
  • #4
haruspex said:
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.
 
  • #5
kostoglotov said:
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).
 

FAQ: Uniform Circular Motion: a concept question

What is uniform circular motion?

Uniform circular motion is a type of motion in which an object moves in a circular path at a constant speed. This means that the object travels the same distance in the same amount of time, resulting in a constant velocity.

What causes uniform circular motion?

Uniform circular motion is caused by a centripetal force, which is directed towards the center of the circular path. This force is necessary to keep the object moving in a circular path, as without it, the object would continue moving in a straight line.

How is uniform circular motion different from linear motion?

Uniform circular motion is different from linear motion in that the direction of motion is constantly changing in circular motion, while it remains constant in linear motion. Additionally, the acceleration in circular motion is directed towards the center of the circle, while in linear motion it is in the same direction as the velocity.

What is the relationship between speed and radius in uniform circular motion?

In uniform circular motion, the speed of the object is directly proportional to the radius of the circular path. This means that as the radius increases, the speed also increases, and vice versa.

How is angular velocity related to linear velocity in uniform circular motion?

Angular velocity in uniform circular motion is the rate at which the object rotates around the center of the circle. It is directly related to linear velocity, as the linear velocity is the product of the angular velocity and the radius of the circular path. This means that as the angular velocity increases, the linear velocity also increases, and vice versa.

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