Physics Help Forum Uniform Circular Motion Acceleration - Plz HELP
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 Oct 7th 2008, 12:24 PM #1 Junior Member   Join Date: Oct 2008 Posts: 1 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 12:54 PM. Reason: Another small question
Oct 9th 2008, 08:28 AM   #2
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 Originally Posted by Maximu5 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

Oct 9th 2008, 03:48 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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 Oct 10th 2008, 09:12 PM #4 Senior Member   Join Date: Apr 2008 Location: HK Posts: 886 Thanks for detailed explanation

 Tags acceleration, circular, motion, plz, uniform

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