Centripetal vs Radial: Explaining Difference to Understand

[coldboyqn]

Can anybody please explain me the difference between "centripetal" and "radial"? I get stuck in distinguishing them!
centripetal force, centripetal acceleration...
radial force, radial acceleration...
I also don't understand why they say that "In uniform circular motion, the difference between 2 velocity vectors at two instant is radial".
Thanks for care.

 

[quasar987]

Can anybody please explain me the difference between "centripetal" and "radial"? I get stuck in distinguishing them!
centripetal force, centripetal acceleration...
radial force, radial acceleration...

A force is radial if the force is always directed along a line that crosses a certain point (the "origin" of the force)

A force is centripetal if it is the cause for keeping the object on which it acts in a uniform circular motion. Since by Newton's second law to every force corresponds an acceleration, we call centripetal acceleration the acceleration associated with a centripetal force. The two are then linked as follow:

"A force is centripetal if and only if it is radial attractive and produces an acceleration on the particle on which it acts of magnitude $a_c=v^2/R$ where v is the --purely tangeantial-- speed of the particle and R is the distance of the particle to the origin of the force. Additionally, if the acceleration is of the above form at anyone time, it will remain so provided no other force acts on the particle [i.e. the circular motion will go on ad vitam eternam]."These are not formal definitions; they're my definitions. It's how I've always intepreted these terms and I never came across something that caused me to question these definitions, so they should be right.

I also don't understand why they say that "In uniform circular motion, the difference between 2 velocity vectors at two instant is radial".
Thanks for care.

Do they say "is radial" or "is tangeantial to the circle"?

 

[vijay123]

hi everybody,
when dealing with rotational motion problems, i tend to think that the centripetal force acts in the outward direction. this idea seems to work in all of my problems but i know that my idea is wrong. can anyone explain the dynamics of this imaginery force?

 

[cesiumfrog]

"Centripetal" presumably translates as headed towards the center. "Centrifugal" as center fleeing.

"Radial" implies radiating outward from the center, although in normal use it doesn't distinguish inward and outward. For that matter, can anyone think of a good term for "an unsigned direction"?

Do they say "is radial" or "is tangeantial to the circle"?

They ought not say tangeantial accelerations give rise to circular motion.

 

[robphy]

"Radial" implies radiating outward from the center, although in normal use it doesn't distinguish inward and outward. For that matter, can anyone think of a good term for "an unsigned direction"?

line?
axis?

 

[coldboyqn]

At http://cnx.org/content/m13871/latest/ I find:

In plain words, uniform circular motion (UCM) needs a force, which is always perpendicular to the direction of velocity. Since the direction of velocity is continuously changing, the direction of force, being perpendicular to velocity, should also change continously.
The direction of velocity along the circular trajectory is tangential. The perpendicular direction to the circular trajectory is, therefore, radial direction. It implies that force (and hence acceleration) in uniform direction motion is radial. For this reason, acceleration in UCM is recognized to seek center i.e. centripetal (seeking center).

This fact is also validated by the fact that the difference of velocity vectors at two instants (Δv) is also radial.

This information seem to be very clear to understand, but, then, they say that:

This proves that centripetal acceleration is indeed radial (i.e acting along radial direction).

(It is inside paragraph discuss about Direction of centripetal acceleration)

It starts the confusion...
I don't really know what do they mention?
Can anyone explain?

 

[Doc Al]

hi everybody,
when dealing with rotational motion problems, i tend to think that the centripetal force acts in the outward direction. this idea seems to work in all of my problems but i know that my idea is wrong. can anyone explain the dynamics of this imaginery force?

"centripetal" just means "toward the center". You are confusing centripetal force, which is due to real forces pulling something towards the center, with centrifugal force. Centrifugal force is an "imaginary" force that is just an artifact of viewing things from a rotating frame of reference. ("centrifugal" means "away from the center".)

When viewing things from the usual inertial frame in which Newton's laws apply, centrifugal forces do not exist.

 

[Doc Al]

Can anybody please explain me the difference between "centripetal" and "radial"? I get stuck in distinguishing them!
centripetal force, centripetal acceleration...
radial force, radial acceleration...

Both "centripetal" and "radial" mean "toward the center". They are just a way of specifying the direction of a vector, like force or acceleration. They mean the same thing, for all practical purposes.

I also don't understand why they say that "In uniform circular motion, the difference between 2 velocity vectors at two instant is radial".

That just means that the difference (which is itself a vector) points in the radial (toward the center) direction, as opposed to the tangential direction. The acceleration in uniform circular motion is centripetal--it points toward the center.

 

[robphy]

Since by Newton's second law to every force corresponds an acceleration, we call centripetal acceleration the acceleration associated with a centripetal force.

Strictly speaking, Newton's Second Law relates the acceleration-of-the-object to the net-force-(the vector-sum-of-forces)-on-the-object. It may be in some cases that you might think to mathematically associate to each applied force its own acceleration, but, pedagogically, it's probably not a good thing to do.

My working definition of "centripetal force" is essentially the radial-component of the net force, which is responsible at that instant for keeping the object in circular motion. In my experience, many students will incorrectly include a "centripetal force" in a free-body diagram, then include it in the vector sum of forces. So, I try to emphasize my working definition.

 

[arildno]

There is a (slight) difference between the concepts "centripetal" and "radial" that has not been commented on:

With "centripetal", we are, CONVENTIONALLY, always talking about a planar phenomenon (2-D), whereas with "radial", we generally may accept 3-D phenomena.

For example, consider a rotating star (say with its axis fixed).
Then, gravity is a radially acting force on any element of the star, but the element experiences a centripetal acceleration about its axis.

 

[coldboyqn]

So, the concepts "centripetal" and "radial" is almost the same but have a small difference that former only for 2-D phenomenon while the later may accept 3-D, right?
But, if that true, while they said that, "This proves that centripetal acceleration is indeed radial (i.e acting along radial direction)"? (Please read the page I mentioned above).

About the difference of two velocity vectors at two instants, I think that this difference is only radial when $$t_1\rightarrow t_2$$, but they said as if it's right for every two different instants... It's so strange!

 

[Doc Al]

But, if that true, while they said that, "This proves that centripetal acceleration is indeed radial (i.e acting along radial direction)"? (Please read the page I mentioned above).

That page is clearly talking about uniform circular motion, which is 2-D.

About the difference of two velocity vectors at two instants, I think that this difference is only radial when $$t_1\rightarrow t_2$$, but they said as if it's right for every two different instants... It's so strange!

Well, if you take the difference for any two instants, t_1 & t_2, you can define an average acceleration. If you assign it to the midpoint between those instants, (t_1 + t_2)/2, then it will be radial as well.

But you are correct. The signficant thing is that the instantaneous acceleration for UCM always points toward the center.

 

[cesiumfrog]

So, the concepts "centripetal" and "radial" is almost the same but have a small difference that former only for 2-D phenomenon while the later may accept 3-D, right?
But, if that true, while they said that, "This proves that centripetal acceleration is indeed radial (i.e acting along radial direction)"?

I think the convention is to only use the term "centripetal" for simple examples of uniform circular motion (which always happens to produce motion in a 2D plane), out of pedagogical desire to distinguish a real force from the apparent "centrifugal" force, and use the term "radial" in all other situations.

Your site tries to prove that "the acceleration required by uniform circular motion" is in the (-ve) radial direction. That's what justifies the convention of choosing to name it as "the centripetal acceleration" in the first place.

 

[coldboyqn]

OK. I think that's enough for me. Thanks for responding. :D