# What is centripital acceleration physically?

1. Dec 30, 2009

### R Power

Hi friends
I know it's a very elementary question but i wat to know what centripital acceleration physically is?
I mean, acceleration is something that results due to any force. In case of centripital acceleration, the force is centripital force (which e.g in case of car making turn is provided by tyres friction) and this force tends to bind the body to revolve around a center.
Now, acceleration is basically, rate of change in velocity along a certain path or distance.
And in case of circular motion the rate of change of angular velocity is angular acceleration,
then what's centriptal acceleration?

2. Dec 30, 2009

### Pythagorean

centripetal means "center seeking". It's not a fundamental force itself, it's more of a scenario that involves a fundamental force.

Orbit is a common example. An object must have the right velocity to orbit Earth. The planet's gravity is pulling it in. Since the velocity is just right, it continues in orbit, always being pulled toward the center of Earth, but never really getting closer.

Notice that the velocity is directed slightly opposite of the force pulling it in. With the right velocity, it's just enough so that it's always correcting itself due to the force, perpetually orbiting.

A more personable example is when you're taking a turn in your car. Your velocity is still going straight, but you're turning the car, so the car's driver side door pushes on you as it turns and makes you turn with it. Here, the door is exerting a centripetal force on you.

Last edited: Dec 30, 2009
3. Dec 30, 2009

### R Power

Yeah, I understand centripital force as you explained too but what I ask is that what is centripital "accleration" physically?

4. Dec 30, 2009

### Staff: Mentor

Velocity has both magnitude (speed) and direction. For circular motion, the centripetal acceleration is the rate of change of the velocity due to its changing direction.

5. Dec 30, 2009

### R Power

that means in case of cars, in case of oversteer we get theorotically infinite lateral or centripital acceleration

6. Dec 30, 2009

### Staff: Mentor

What makes you think that?

7. Dec 30, 2009

### tiny-tim

geometry, not physics

Hi R Power!
It isn't.

Centripetal (same root as "petition", from the Latin for "seek" ) acceleration is geometry, not physics.

Anything going along a curve has a centripetal acceleration equal to speed squared over radius of curvature.

8. Dec 30, 2009

### Pythagorean

The same vector conventions apply to the acceleration. As Doc Al said, a change in direction of velocity is an acceleration (so is a change in magnitude, of course, like when you speed up on a straight road).

Using the vector conventions, you can see how the velocity of the object changes at every point around it's orbit (because of the centripetal force acting on it).

Last edited: Dec 30, 2009
9. Dec 30, 2009

### R Power

in case of cars lateral acceleartion is dependent upon square of velocity as well as cornering stiffness constant (which is directly related to slip angles of rear and front wheels). In case of oversteer slip angles of rear wheels are greater so CSC becomes negative and at critical speed it becomes 1 and when we relate it to lateral acceleration
through a certain derived formula we get infinite lateral acceleration.

You may not understand the above text if you don't have considerable knowledge of vehicle dynamics.
I was just confused what infinite centripital acceleration means, and now I just undestand that infinite acc will create a slip.

10. Dec 30, 2009

### rcgldr

Centripetal acceleration just means an acceleration that is perpendicular to an objects current direction. The resulting path will be circular or spiral like. One example of a spiral like path produced by centripetal acceleration is called involute of circle, which is the path of an object connected to a string that winds or unwinds around a post.

http://mathworld.wolfram.com/Involute.html

A car can only experience a finite amount of centripetal acceleration, regardless of oversteer. Oversteer has two basic meanings. One usage is when the rear tires have more slip angle than the front tires, a situation that only exists when a driver is countersteering in the direction of a drift or skid. The other usage describes the tendency for the rear end to drift or slide more than the front end while turning near the limits of traction.

Last edited: Dec 30, 2009
11. Jan 2, 2010

### DannoXYZ

If you draw a picture of a car traveling in a straight line from above, this is easier to understand. Draw a straight behind and in front of it depicting the path of the tyres on the ground.

Then under cornering when centripetal forces make it go in a circle, you'll notice that the path carved by the tyres is circular. Centripetal force in this case, is from the tyres pushing the car away from its straight-line path into a circle. The force you feel as a passenger is the seat and car-door pushing in from the outside and making you go in a circle. In the case of a rear-seat passenger who isn't paying attention, this force can come from the window against their face.

There's some equations for you in this Physics of Racing chapter.

Last edited: Jan 2, 2010
12. Jan 5, 2010

### makyol

mV^2/R = ma => a= V^2/R This is basically centripetal acceleration, in case if you are really asking this.

13. Jan 6, 2010

### Dosmascerveza

From what I understand centripetal acceleration is the type of acceleration that causes circular motion. For example of you swing a yo yo around your head the direction is constantly changing and therefore so is the velocity, if the velocity is changing then the yoyo has an acceleration. Now as for the direction of this acceleration? well if the yo yo is being swung in a circle it is pointing inward down the line of the yo yo toward your hand. So the acceleration vector points along the radial line voila.

To show this more rigorously . Choose a point P on a path of circular motion and draw its velocity tangent to the path of motion. notice the angle theta swept out by the velocity vector as it changes by magnitude delta v is the same angle as is swept out but magnitude of v during a change in time dt and so you can write (d v)/v =v(d t)/r and it follows that dv/dt=v^2/r this is the expression for centripetal acceleration. Like someone already stated, its a consequence of the geometry of the situation. Angular acceleration, however is a direct measure of how fast the rate of rotation wrt time.

14. Jan 7, 2010

### R Power

I do not get it properly, can you explain a bit more in detail.
I am confused that what is the need for defining centripital acceleration. Rate of change of direction can be given by angular acceleration also because angular acceleration is rate of change of angular velocity as well as direction!

15. Jan 7, 2010

### Staff: Mentor

Centripetal acceleration is not the rate of change of direction--it's the rate of change of velocity due to changing direction. For an object in uniform circular motion, the angular acceleration is zero but the centripetal acceleration is certainly not zero.

Here's a derivation of the centripetal acceleration formula: http://hyperphysics.phy-astr.gsu.edu/HBASE/cf.html#cf2"

And another version of the same thing: Derivation of the Formulas for Centripetal Acceleration

Last edited by a moderator: Apr 24, 2017