What are the Two Forms of Acceleration in Circular Motion?

[Raza]

I know the equation (\frac{v^2}{r}) but what is the description of radial acceleration? I saw couples of internet sites but I don't get it. Can someone explain it to me in a dull way and use typical examples of this?

Thanks

 

[Doc Al]

"Radial" just means "along the radius" or towards the center (also called centripetal). Realize that velocity--a vector--can change (accelerate) either by changing magnitude or direction or both. For something going in a circle you can express the acceleration as having a tangential component (changing magnitude, tangent to the circle) and a radial component (changing direction, towards the center).

The expression \frac{v^2}{r} gives the radial component of acceleration for something going in a circle. To see where such a formula comes from, look here: http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html#cf2"

 

[Raza]

I don't get it. I am a person who needs to visualize thing in order to get things. That's why I need an example.

 

[arildno]

Well, visualize a circle with a radius, then.

 

[Raza]

haha funny.

 

[Raza]

Reading the link that Doc Al gave (awesome link, by the way.I bookmarked it), I get an example in my head. Suppose I spread my hand outward and started spinning around; A lot of blood would become relocated to my fingertip. So the Centripetal force is keeping my blood from coming outside of my finger. Right?
Please respond

 

[Doc Al]

Sure, but let's keep it even more basic. You're spinning around, hands extended. What direction are your hands moving in at any given moment? They are moving tangential to the circle you are spinning in. Recalling Newton's 1st law, if there were no force acting on your hands they would continue moving in a straight line. But of course they don't--they move in a circle--because you are exerting a force on your hands. The force that pulls them into a circular motion (instead of continuing to move straight) is called the centripetal force. (In this case it's your arm that pulls your hands inward--they are attached, you know. )

Make sense?

 

[Raza]

Yes, I finally got Centripetal force (thank you) but what is Centripetal acceleration? I know you guys are getting annoyed with these questions but please help the needy

 

[Cyrus]

Are you familiar with what a vector is?

 

[Raza]

yes, scalar is something with no directions (ex.speed) and vector is something with directions (ex.velocity)

 

[Cyrus]

Are you familiar with what acceleration is, in terms of vectors?

 

[Raza]

no, I am not familiar with what acceleration is, in terms of vectors.

 

[Cyrus]

The acceleration manifests itself in two possible forms. The first form is an actual change in the magnitude of the velocity (think of the velocity vector as increasing or decreasing in length, but pointing in the same direction).

The other possible acceleration occurs when the velocity vector maintains its magnitude but changes its direction. This is consistent with our notion of acceleration because there is a still change in velocity (this time the change is direction, and not magnitude).

When you are moving in a circle with constant tangential velocity, the direction of the velocity vector always changes as the particle moves but maintains its magnitude |v|. So your equation is a=|V|^2/R.

The direction of this acceleration will always point towards the center of the circle.

I would recommend you grab a physics book (Sears and Zemanski, or halliday and resnik) and read the first two chapters. It will give you a sufficient answer.