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Old Oct 7th 2008, 01:24 PM   #1
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Arrow Uniform Circular Motion Acceleration - Plz HELP

Hi I'm looking at accerleration for uniform circular motion. My textbook shows the derivation to arrive at the equation: acceleration = (v^2/r, toward centre of the circle). In other words this is the centripetal acceleration.

1.) At the first step in the derivation the book claims that dv = v*(dθ). What do these variables represent? θ was defined earlier as the angular position so dθ is the derivative of the angular position which is...what?

2.) I thought ω was the symbol for angular velocity. So what are v and dv?

3.) There's another equation used in the book: v = ωr. Does this mean the tangential velocity is equal to the angular velocity multiplied by the radius?

Thanks so much

Last edited by Maximu5; Oct 7th 2008 at 01:54 PM. Reason: Another small question
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Old Oct 9th 2008, 09:28 AM   #2
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Originally Posted by Maximu5 View Post
Hi I'm looking at accerleration for uniform circular motion. My textbook shows the derivation to arrive at the equation: acceleration = (v^2/r, toward centre of the circle). In other words this is the centripetal acceleration.

1.) At the first step in the derivation the book claims that dv = v*(dθ). What do these variables represent? θ was defined earlier as the angular position so dθ is the derivative of the angular position which is...what?

2.) I thought ω was the symbol for angular velocity. So what are v and dv?

3.) There's another equation used in the book: v = ωr. Does this mean the tangential velocity is equal to the angular velocity multiplied by the radius?

Thanks so much
1) dθ you may thought as a very small change in the angle.For v which represents the velocity. For small change of velocity and θ, the equation of θ=s/r can be applied, where s is the arc length and r is the radius of circle.

2) ω is the symbol for angular frequency which is not the same as angular velocity. v is the velocity aforementioned. dv means a very small change in velocity.

3)It means the tangential velocity is equal to the angular FREQUENCY multiplied by the radius.ω= 2pi (f) where f is the number of rotations per second
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Old Oct 9th 2008, 04:48 PM   #3
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Maximu5: I thought ω was the symbol for angular velocity.
werehk:ω is the symbol for angular frequency which is not the same as angular velocity. v is the velocity aforementioned. dv means a very small change in velocity.
wikipedia:Angular velocity is usually represented by the symbol omega (Ω or ω).
wikipedia:In physics (specifically mechanics and electrical engineering), angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, and radian frequency) is a scalar measure of rotation rate.
So it seems that $\displaystyle \omega$ is used to express both angular velocity and angular frequency. But I agree with werehk that your book means
3)It means the tangential velocity is equal to the angular FREQUENCY multiplied by the radius.
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Old Oct 10th 2008, 10:12 PM   #4
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Thanks for detailed explanation
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