Uniform Circular Motion: Centripital Acceleration vs. Acceleration

In summary, there are two equations for acceleration in uniform circular motion: a=v^2/r and a=4pi^2r/T^2. These equations are equivalent, as the speed can be expressed as 2pi*r/T. This means that the acceleration of the object is centripetal, or directed towards the center of the circle. Both equations can be used to solve problems in uniform circular motion.
  • #1
Chele
17
0
I am very new to physics and am taking a my first University Physics class. This is not a call for a problem to be solved, but a clarification on terminology.

In solving problems for uniform circular motion, some problems call for the acceleration of the object (a=v^2/r) and others the centripital or instantanious acceleration (a=4pi^2r/T^2).

Can you please attempt to explain, in layman's terms, the difference between the two references to acceleration?

Thanks for your assistance.
 
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  • #2
Chele said:
In solving problems for uniform circular motion, some problems call for the acceleration of the object (a=v^2/r) and others the centripital or instantanious acceleration (a=4pi^2r/T^2).
The two formulas are equivalent. (Express the speed in terms of circumference over period and you'll see for yourself.)

For uniform circular motion, the acceleration is centripetal. (Centripetal just means "towards the center".)
 
  • #3
Wow- I'll need to look at that in further detail... :yuck:
Thanks for your help!
 
  • #4
Chele said:
Wow- I'll need to look at that in further detail... :yuck:
Thanks for your help!

Indeed, the two are equivalent for UCM. This can be seen easily if you recall that for constant speed, you may use v= distance/time. If you wait for the particle to go through a full circle, it will have covered a distance 2 Pi r, and the time elapsed will be the period T.
So

[itex] v_{ucm} = \frac{2 \pi r}{T} [/itex]

Using this formula it is simple to prove that the two equations for acceleration you gave are equal.
 
  • #5
Okay, thanks. I worked it out and it is exactly the same. Not sure why I didn't see it before. Thanks guys!
 

1. What is the difference between centripital acceleration and acceleration?

Centripital acceleration is the acceleration towards the center of a circular path, while acceleration is the change in velocity over time. Centripital acceleration is always perpendicular to the velocity, while acceleration can be in any direction.

2. How is centripital acceleration calculated?

Centripital acceleration can be calculated using the formula a = v^2/r, where a is the centripital acceleration, v is the velocity, and r is the radius of the circular path.

3. What is the relationship between centripital acceleration and speed?

The greater the speed of an object moving in a circular path, the greater the centripital acceleration needed to keep it in that path. This means that as speed increases, the centripital acceleration also increases.

4. Is centripital acceleration the same as centripital force?

No, they are not the same. Centripital acceleration is the acceleration towards the center of a circular path, while centripital force is the force that causes this acceleration. Centripital force is usually provided by tension, gravity, or friction.

5. Can an object have centripital acceleration without a change in speed?

Yes, an object can have centripital acceleration without a change in speed if the direction of its velocity is constantly changing. This means it is constantly changing its direction but not its speed, resulting in a centripital acceleration towards the center of its circular path.

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