# Centripetal force

## Main Question or Discussion Point

I am writing an essay in which I try to describe Centripetal Force to a layperson. Since I am a layperson myself, I wanted to make sure that there were no glaring errors before I submitted it. If someone could review this, and let me know if it passes scientific muster, I would appreciate it. Thanks.

That seer of seers Sir Isaac Newton observed that any motion in a curved path represented accelerated motion---and thus required a force directed towards the center of the path, otherwise known as Centripetal Force (not to be confused with its popular cousin Centrifugal Force, which means something else entirely and shall not be mentioned again).

Centripetal Force is a term that suffers from the confusion between Speed and Velocity. So here now is the official difference between Speed and Velocity:

If you’re in a car going 30 miles per hour in a straight line, then 30 mph is both your Speed and your Velocity.

If, however, you’re in a car going 30 mph in a straight line, then make a 30 mph left turn, your Speed is still 30 mph, but your Velocity has increased, because Velocity measures your rate of motion plus the change in your direction of motion.

So a race car driver might be driving in circles at a constant speed of 200 mph, but by definition he is actually accelerating (i.e., increasing his velocity) the whole time. Basically, if you’re covering more area at the same speed, a C instead of an I, some component of the equation must also be increasing. This component is called Velocity. It’s like Speed in three-dimensions. The greater the curve, the more you have to accelerate to cover the same amount of distance in the same amount of time. The moral of the story is, When turning, you’ve got to accelerate just to keep up.

So for an object to orbit at a constant speed around another object---the Earth turning around the Sun, the Moon turning around the Earth, an electron turning around a nucleus---it must be accelerating. An orbiting object, moving in a circle---turning around a central point---can be said to be accelerating inwards towards that point.

According to Newton’s Second Law of Motion (the No Freebies clause), an object that accelerates must therefore be getting some kind of push in the direction of the acceleration. And if this object is accelerating inwards, ergo, there must be an inwardly-directed force acting upon it. This push towards the center is called “Centripetal Force”. The word centripetal literally means center-seeking.

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Hootenanny
Staff Emeritus
Gold Member
If you’re in a car going 30 miles per hour in a straight line, then 30 mph is both your Speed and your Velocity.
Okay, but in my honest opinion velocity is meaningless in straight-line (curvilinear) motion.
If, however, you’re in a car going 30 mph in a straight line, then make a 30 mph left turn, your Speed is still 30 mph, but your Velocity has increased, because Velocity measures your rate of motion plus the change in your direction of motion.
Not entirely true, in this case to say one's velocity has 'increased' is incorrect. It is true that one component of the velocity would increase (to 30mph), however, another component would decrease (to zero). In general it's a bad idea to talk about an object's velocity increasing or decreasing.

Furthermore, it is better to say that acceleration is the rate of change of velocity, or that acceleration is a measure of how fast one's velocity it changing. An accelerating object does not necessarily increase it's speed, specifically an object in circular motion, is constantly accelerating towards the centre of the circle but never gets there, nor does it's speed ever change. The only thing that changes is the direction in which it's traveling, it's this change in direction that requires an acceleration.

I wish I had more time to type up a complete response, perhaps tonight I'll be able to add more.

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The part about the distinction between speed and velocity must be rectified.

If you’re in a car going 30 miles per hour in a straight line, then 30 mph is both your Speed and your Velocity.
No. 30mph is only the speed - the magnitude of the velocity. A vector (velocity, in this case) contains two parts: magnitude and direction. So, here, you'd have to say the velocity is 30mph + information about the direction (towards North, say). If there was another car going 30mph in the opposite direction, in a straight line, it's speed would also be 30mph, but it's velocity would be 30mph towards South. (Mathematically, the North and South are written in terms of unit vectors in some coordinate system.)

If, however, you’re in a car going 30 mph in a straight line, then make a 30 mph left turn, your Speed is still 30 mph, but your Velocity has increased, because Velocity measures your rate of motion plus the change in your direction of motion.

So a race car driver might be driving in circles at a constant speed of 200 mph, but by definition he is actually accelerating (i.e., increasing his velocity) the whole time.
The velocity has not increased. Acceleration can occur in three different circumstances:

Increase in speed (magnitude of velocity),
change in direction, or
a combination of the two.

While an acceleration can mean an increase in the magnitude of the velocity, in general it denotes only a change as mentioned above. (It's the rate of change of velocity with respect to time - the rate could increase or decrease. Sometimes, people use the term deceleration to refer to negative acceleration.) After all, how can you "increase" the direction? And by your logic, turning right would imply decreasing velocity, which is obviously false.

Basically, if you’re covering more area at the same speed, a C instead of an I, some component of the equation must also be increasing. This component is called Velocity. It’s like Speed in three-dimensions.
Hmm...an object has a velocity even when moving in a straight line, and it can increase even then. And "speed in three dimensions" is an oxymoron. Thanks for the feedback

Obviously, I am one of those still confused by the difference between speed and velocity! For instance

Not entirely true, in this case to say one's velocity has 'increased' is incorrect. It is true that one component of the velocity would increase (to 30mph), however, another component would decrease (to zero).

Which component would that be? The magnitude? Meaning the direction increases to 30mph and the magnitude decreases to 0? Something's still not registering for me here.

I guess my terminology is a little broad. For my purposes, which is to give a layman's definition of centripetal force, and not a physicist's definition, I'd like to steer clear of such terms as magnitude of velocity or unit vectors, which might cause the reader's eyes to glaze over. But I still don't want to put in any wrong information. So if I omitted the offending passages, would my definition make sense?

That seer of seers Sir Isaac Newton observed that any motion in a curved path represented accelerated motion---and thus required a force directed towards the center of the path, otherwise known as Centripetal Force (not to be confused with its popular cousin Centrifugal Force, which means something else entirely and shall not be mentioned again).

Centripetal Force is a term that suffers from the confusion between Speed and Velocity. So here now is the official difference between Speed and Velocity:

If you’re in a car going 30 miles per hour in a straight line, then 30 mph is both your Speed and your Velocity.

If, however, you’re in a car going 30 mph in a straight line, then make a 30 mph left turn, your Speed is still 30 mph, but your Velocity has increased, because Velocity measures your rate of motion plus the change in your direction of motion.

So a race car driver might be driving in circles at a constant speed of 200 mph, but by definition he is actually accelerating the whole time. The greater the curve, the more you have to accelerate to cover the same amount of distance in the same amount of time. The moral of the story is, When turning, you’ve got to accelerate just to keep up.

So for an object to orbit at a constant speed around another object---the Earth turning around the Sun, the Moon turning around the Earth, an electron turning around a nucleus---it must be accelerating. An orbiting object, moving in a circle---turning around a central point---can be said to be accelerating inwards towards that point.

According to Newton’s Second Law of Motion (the No Freebies clause), an object that accelerates must therefore be getting some kind of push in the direction of the acceleration. And if this object is accelerating inwards, ergo, there must be an inwardly-directed force acting upon it. This push towards the center is called “Centripetal Force”. The word centripetal literally means center-seeking.

Hootenanny
Staff Emeritus
Gold Member
Hi utek1,

From reading your post, it seems that you yourself still have fundamental problems with the concepts of speed, velocity and acceleration. Unfortunately, I haven't the time for a detailed response this evening, but I should have some free time in the morning.

In the meantime, I suggest that you re-read neutrino's post and take heed of his comments.

rcgldr
Homework Helper
Obviously, I am one of those still confused by the difference between speed and velocity!
Speed is a scalar with no direction implied. Velocity is a vector with two components, a directon, and a speed.

Not entirely true, in this case to say one's velocity has 'increased' is incorrect. It is true that one component of the velocity would increase (to 30mph), however, another component would decrease (to zero).

Which component would that be?
Assume the car is heading north at 30mph. It's north/south component of velocity is +30 mph, and it's west/east component of velocity is 0 mph. After completing the left turn, it's north/south component of velocity is 0 mph, and it's west/east component of velocity is +30 mph.

Acceleration (or deceleration) just causes a change in velocity, not always an "increase".

OK, I think I'm starting to get the hang of these terms. Magnitude of velocity---that's another word for speed---how fast---and the directional vector measures the degree that one is turning---how sharp.

What I was trying to get at in my example was that the car was going north/south degrees in a straight line (its directional vector being 0) at 30 mph (its magnitude), and then he makes a 90 degree left turn, also at 30 mph, his velocity would increase. In real life, turning sharply without slowing down might cause you to skid off the road, but what I wanted to show was that while the speed of the car remained constant, which is to say that it's magnitude of velocity remained the same, while it was turning, the angle (or directional vector) was greater by 90 degrees, and so its velocity increased correspondingly, which meant that it must be accelerating to achieve this affect. Once the car was going straight again in an east/west direction, it's magnitude of velocity would still be 30mph, but it's directional vector would go back to zero, or perhaps more appropriately, decelerated to 0. Anyway, this is how I currently understand it.

I'm really trying to use as many ordinary terms as possible here, because for the average reader, words like "magnitude" stand for different things than they do in science. It's almost a value judgement in people's minds which I'd like to avoid. "Acceleration" in particular is associated with going faster---increasing velocity---even if to a physicist it can stand for any old change in direction. I appreciate you taking me to task for not using the exact terminology, but in this case I am trying to draw a picture for a layperson to visualize more than I am trying to write a textbook. And the picture I am trying to paint is that velocity is a combination of speed plus change of direction, and this plus, this additional force, is referred to as Centripetal Force. If the picture is right but the terms are sketchy, I can live with that. If the picture is wrong---that I'm fundamentally misrepresenting something---then I'm screwed.

Hootenanny
Staff Emeritus
Gold Member
OK, I think I'm starting to get the hang of these terms. Magnitude of velocity---that's another word for speed---how fast---
Yes, good and the directional vector measures the degree that one is turning---how sharp.
Not quite, the direction literally tells you in which direction the object is traveling, the object need not be "turning" to have a direction. Velocity, as you are aware, is a vector quantity, which in simple terms means it must have a direction and magnitude at all times
What I was trying to get at in my example was that the car was going north/south degrees in a straight line (its directional vector being 0) at 30 mph (its magnitude), and then he makes a 90 degree left turn, also at 30 mph, his velocity would increase.

In real life, turning sharply without slowing down might cause you to skid off the road, but what I wanted to show was that while the speed of the car remained constant, which is to say that it's magnitude of velocity remained the same, while it was turning, the angle (or directional vector) was greater by 90 degrees, and so its velocity increased correspondingly, which meant that it must be accelerating to achieve this affect. Once the car was going straight again in an east/west direction, it's magnitude of velocity would still be 30mph, but it's directional vector would go back to zero, or perhaps more appropriately, decelerated to 0. Anyway, this is how I currently understand it.
Once again no! The velocity of the car has not increased, rather the car has simply changed direction, it's magnitude has remained constant. As has been stated previously there are two circumstances under which an object accelerates,
• A change in direction
• A change [increase/decrease] in speed
Of course, any combination of the two also produces an acceleration. Furthermore, your angle is not a direction vector, the angle simple indicates the direction in which the car is traveling. Also, please note that for a given coordinate system the point from which your angle is measured must remain constant.

For example, consider again your car traveling north/south as you say. For convenience, let us define the angle to be measured anti-clockwise from the north-south direction. So, you car's initial velocity is 30 mph heading north-south. Alternatively, one could also give the velocity as 30 mph heading 0o. Then suppose you make a 90o left turn, your new velocity would be 30 mph heading west-east or 30 mph heading 90o. In this description, the orange parts is the magnitude (speed) and the purple parts is the direction. Note that neither the speed nor direction are themselves vectors, but together they constitute the velocity vector.
I'm really trying to use as many ordinary terms as possible here, because for the average reader, words like "magnitude" stand for different things than they do in science. It's almost a value judgement in people's minds which I'd like to avoid. "Acceleration" in particular is associated with going faster---increasing velocity---even if to a physicist it can stand for any old change in direction. I appreciate you taking me to task for not using the exact terminology, but in this case I am trying to draw a picture for a layperson to visualize more than I am trying to write a textbook. And the picture I am trying to paint is that velocity is a combination of speed plus change of direction, and this plus, this additional force, is referred to as Centripetal Force. If the picture is right but the terms are sketchy, I can live with that. If the picture is wrong---that I'm fundamentally misrepresenting something---then I'm screwed.
I understand that terms used in physics have different popular meanings, and believe me, it something that irritates the hell out of me. However, that said a popular science article should be both informative and engaging to the layperson; yes, the article may misrepresent some of the more subtle nuances, but article should be fundamentally correct. Furthermore, it really isn't difficult to define acceleration as the change in velocity, whether that be in direction or speed. Nor is it difficult to define velocity as speed with direction, I'm sure that with some simple examples even a person with no former physics experience could grasp the concepts.

Ok, looks like it's back to the ol' drawing board. Physicists have gone to a lot of trouble to give certain terms exact definitions, and far be it from me rock the boat.

What I've learned so far is this. Velocity measures how fast something moves and which way something points, and just because you've changed which way something points that doesn't mean the velocity has increased, it just means it has changed. It's not necessarily an additive function. Using "increase" or "decrease" to describe velocity is like stepping into a minefield.

Acceleration is also a tricky term to use. Since acceleration measures a change in velocity, and velocity is a two-part definition, a change in acceleration might be a change in an object's speed (aka its magnitude), or it might be a change in which way its pointing (its directional vector). For something to accelerate, it doesn't necessarily mean it's going faster. It might be going at the same speed. It might even mean it's going slower. As long one of the components of velocity--speed and/or direction---has changed, you've accelerated.

For all this, at least one line in my original post still seems to be true:

The greater the curve, the more you have to accelerate to cover the same amount of distance in the same amount of time.

ls this still a legitimate thing to say, or does it go into the dumpster with the rest of the text?

By the way, thanks to all for taking the time to correct scientifically ignorant souls like myself.

Hootenanny
Staff Emeritus
Gold Member
Velocity measures how fast something moves and which way something points, and just because you've changed which way something points that doesn't mean the velocity has increased, it just means it has changed. It's not necessarily an additive function. Using "increase" or "decrease" to describe velocity is like stepping into a minefield.

Acceleration is also a tricky term to use. Since acceleration measures a change in velocity, and velocity is a two-part definition, a change in acceleration might be a change in an object's speed (aka its magnitude), or it might be a change in which way its pointing (its directional vector). For something to accelerate, it doesn't necessarily mean it's going faster. It might be going at the same speed. It might even mean it's going slower. As long one of the components of velocity--speed and/or direction---has changed, you've accelerated.
Much better For all this, at least one line in my original post still seems to be true:

The greater the curve, the more you have to accelerate to cover the same amount of distance in the same amount of time.

ls this still a legitimate thing to say, or does it go into the dumpster with the rest of the text?
Sounds roughly right if I have interpreted it correctly. By the way, thanks to all for taking the time to correct scientifically ignorant souls like myself.
No problem, it's a pleasure. Just out of interest, is this a school project? If so, which subject is it for?

I work with high school small learning communities. It's an interdisciplinary curriculum, with courses cross-pollinating.

Hootenanny
Staff Emeritus