Physics Help Forum Uniform Circular Motion Acceleration - Plz HELP

 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
Senior Member

Join Date: Apr 2008
Location: HK
Posts: 886
 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
Senior Member

Join Date: Apr 2008
Posts: 815
 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.
.
__________________
Isaac
If the problem is too hard just let the Universe solve it.

 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

 Thread Tools Display Modes Linear Mode

 Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post mido22 Advanced Mechanics 2 Jan 9th 2014 11:39 PM centenial Kinematics and Dynamics 1 Sep 15th 2010 06:08 PM vinson24 Periodic and Circular Motion 4 Sep 14th 2010 11:38 AM phys30 Periodic and Circular Motion 2 Oct 7th 2009 09:48 PM devanlevin Advanced Mechanics 0 Nov 13th 2008 10:36 PM