# Why does (dr/dt)*θ = 0 when deriving Velocity?

1. Feb 9, 2012

### LearninDaMath

The problem statement, all variables and given/known data

A derivation of Instantaneous Velocity

Arc length = s = θ * r

ds/dt = d(θr)/dt = Instantaneous V

Product rule:

V$_{t}$ = (dθ/dt)*r + (dr/dt)*θ

V$_{t}$ = (dθ/dt)*r + 0

V$_{t}$ = ωr

Question:

Why does dr/dt*θ = 0 ?

2. Feb 9, 2012

### xlava

Since r is constant, the rate of change of the radius with respect to time (or anything for that matter) is going to be 0.

3. Feb 9, 2012

### LearninDaMath

ah makes perfect sense, thanks.

4. Feb 9, 2012

### xlava

No problem, sir. Good luck.