Understanding Centripetal Acceleration: Explained with Easy-to-Follow Graphics

[Earn Success]

According to my book, in centripetal acceleration, the direction of the velocity is the same as the acceleration, which points towards the center. There is a picture of a velocity vector pointing out of the circle, and then another point with a second vector pointing out, and the resultant in a different picture. The resultant goes between them which I get, but why does it go towards the middle of the circle? This is more of a vector question I guess. By the way I got a 67 on the Vector test



I can memorize the idea all I want, but I don't really understand how the book explains this, and I want someone to put a picture more suited for beginners because the book really confuses me. Sorry if this is really silly

 

[JaredJames]

The centripetal acceleration is towards the middle of the circle and is a function of the objects tangential velocity and the radius of the circle.

Centripetal Acceleration = Tangential Velocity Squared / Radius

A bit off topic you say, well it brings me onto the next point for you:

Now, I'm going to pass you to this book as it explains things far better than I ever could for you. It is regarding the tangential velocity -

http://docs.google.com/viewer?a=v&q...EIJCzF&sig=AHIEtbQjMXtV-lppfXzTctaQFCG9rDxf3A

Personally, I'm not happy with using the word velocity on its own as you'll see in most places as velocity requires a speed and direction. In a circle, the direction of motion is constantly changing and so the velocity is constantly changing. Hence, tangential velocity.

 

[Earn Success]

I think vectors just completely confuse me. What if they used instantaneous velocity, then there would be no resultant vector...

As soon as I was about to say, "and no acceleration" I realized that then there would be no acceleration with only 1 vector. Ok so I get that, but after reading several guides and my book, the vector things is so weird that I will never understand it. You take 2 velocities going in the completely opposite direction of the result? That sounds made up to me

 

[JaredJames]

Velocity is speed with a direction. It is a vector.

The tangential velocity, during rotation is an instantaneous velocity. It is the velocity at a specific point during the rotation and it is always perpendicular to the centripetal acceleration.

 

[Earn Success]

Yes but then it says the change in V-> points towards the center of the circle. That v is is that makes the acceleration happen right? And that v is towards the center because of some sort of vector subtraction which I can never comprehend

 

[JaredJames]

Did you read the link I posted? It is extremely simple and explains the concept rather well in my opinion. It has both ways of calculating the centripetal acceleration and explains the vectors required in detail.

 

[Earn Success]

i understand it but i don't think it makes a bit of sense that you can subtract invisible things

 

[JaredJames]

Invisible?

 

[gomunkul51]

Personally, I'm not happy with using the word velocity on its own as you'll see in most places as velocity requires a speed and direction. In a circle, the direction of motion is constantly changing and so the velocity is constantly changing. Hence, tangential velocity.

I see no contradiction between the definition of velocity the fact that it changes.
This coincides exactly with what is happening, the velocity really is changing constantly but only it's "direction" part is changing and not it's "size" (modulus) !

e.g. vectors (1,2) and (2,1) have the same size but different directions.

 

[JaredJames]

So they are not (or wouldn't be) equal velocities. Your point is?

 

[gomunkul51]

my point is that when you choose the directions: radial and tangential to represent a vector, then the velocity is the same in size and direction.
you were thinking in Cartesian coordinates my friend, no one forces you to use them.

 

[JaredJames]

then the velocity is the same in size and direction.

So if I swing a bucket with water in a circle, the direction of the velocity at the 9 o'clock position is equal to the direction of the velocity at the 3 o'clock position?

Velocity has two parts. If you change one, you alter the velocity. The magnitude may not change, but the velocity will. Or are you telling me the velocity of 10m/s North has the same direction as 10m/s South?

 

[tiny-tim]

Hi Earn Success!

There is a picture of a velocity vector pointing out of the circle, and then another point with a second vector pointing out, and the resultant in a different picture. The resultant goes between them which I get, but why does it go towards the middle of the circle? … By the way I got a 67 on the Vector test

You get that the "resultant", as you call it, goes between them, ie into the circle, but you can't see that symmetry means it has to go towards the centre?

I suspect that you're trying to add the tail of the second vector tot he head of the first vector … then the "resultant" goes from the tail of the first to the head of the second vector, which is into the circle, but only a little … is that what's bothering you?

If so, it's because you should be adding the tail of the second vector to the tail of the first vector …

to subtract vectors (ie to find a vector c = a - b, you need b + c = a, a triangle abc in which the arrows point along a, or along b and c), you must start both vectors at the same place.

And the acceleration isn't the "resultant" of the velocity vectors, it's the difference between them.

(I suspect your poor marks are because you're joining your vectors to make the wrong triangles … any pair of vectors a and b can be put together to make two different triangles, and it's important to know which is the correct one )

 

[gomunkul51]

So if I swing a bucket with water in a circle, the direction of the velocity at the 9 o'clock position is equal to the direction of the velocity at the 3 o'clock position?

Velocity has two parts. If you change one, you alter the velocity. The magnitude may not change, but the velocity will. Or are you telling me the velocity of 10m/s North has the same direction as 10m/s South?

Yes. They are both in the tangential direction.
are vectors (1,1) and (2,2) in the same direction? you would say yes, and you are right but only Cartesian coordinate system. Those two vectors are NOT in the same direction if you are in polar coordinate system. There are many other coordinate systems where they aren't in the same direction.
All I am trying to say is that the velocity is the same in size and direction in the polar coordinates so you don't have anything to worry about the original normal acceleration definition.