What does a=v^2/r mean
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What does a=v^2/r mean

[From: ] [author: ] [Date: 13-07-04] [Hit: ]
I am easily able to understand this math & physics, but I just simply dont get the result of the equation. I understand its use is to calculate the centripetal acceleration of something traveling in a circle and that it is somehow used to calculate the acceleration of direction. I also understand an object moving in a circle is constantly accelerating because it is constantly changing its direction. Here is an example of what I am confused about.A ball is rolling in a circle with a constant velocity of 5m/s.......
I am completely confused on this equation. Normally, I am easily able to understand this math & physics, but I just simply don't get the result of the equation. I understand its use is to calculate the centripetal acceleration of something traveling in a circle and that it is somehow used to calculate the acceleration of direction. I also understand an object moving in a circle is constantly accelerating because it is constantly changing its direction. Here is an example of what I am confused about.
A ball is rolling in a circle with a constant velocity of 5m/s. The radius of the circle is 5m.
a = 5m/s^2/5m
a = 25m^2/s^2/5m
a = 5m/s/s or 5m/s^2
But it is moving with a constant speed so it cannot be accelerating 5m/s every second? This is what I am confused about.
Thank you, best answer will get best answer. :)

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Centripetal acceleration points towards the center of the circle the ball is rolling around. In this case, the ball is accelerating towards the center at 5m/s^2. (If you multiply this by the ball's mass, you will get the force acting on the ball that is forcing the ball towards the center -- this is why the ball is going in a circle; otherwise it would just go in a straight line!)

You would be correct when you say, "The ball is moving in a constant speed and therefore cannot be accelerating" if the ball was moving in a straight line. However, linear acceleration is different from centripetal acceleration. If the ball was going in a straight line at 5 m/s there would be no acceleration, but the ball is not going in a straight line; it is continuously turning (continuously changing direction), and therefore has an acceleration! Hope this helps! :)

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F = m * a
a = F ÷ m
The direction of the acceleration is the same as the direction of the force.

Centripetal force = m * v^2 ÷ r
Centripetal acceleration = v^2 ÷ r
The direction of the centripetal acceleration is the same as the direction of the centripetal force.
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