# Angular Velocity Calculation

1. Jun 19, 2016

### Nikstykal

1. The problem statement, all variables and given/known data

2. Relevant equations
v = w x r

3. The attempt at a solution
I got the answer correct after a few tries, but I am little confused on why it has to solved this specific way. I know that v = w x r, so why can I not just say w = v/r? Is it because w is measured from the center of the roller so v = w x r would be vcenter, not vtop?
That is how I ended up solving it, but I wanted to make sure I didn't get there "accidentally" or misinterpreted the process.

Using that diagram and concept of similar triangles:
tan θtop = tan θcenter
Stop/2r = Scenter/r
Stop = 2*Scenter, Scenter = rθ
Stop = 2rθ
d(Stop)/dt = vtop = d(2rθ)/dt = 2rθ' = 2rωtop
thus, ω = v/2r

Any reasoning as to why I have to do this would be much appreciated!!

2. Jun 19, 2016

### tommyxu3

That's for the centro of the motion is at the bottom of the roller. Your formula should be applied as $v=2r\cdot\omega,$ where $2r$ is the distance from the bottom to the top.

3. Jun 20, 2016

### Nikstykal

Ahh, i forgot, when using v = w x r you have to always measure from from IC unless using relative velocity equation. Thank you!