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