# Stuck on a problem

1. Jan 19, 2005

### DMD

Here's the problem:

A uniform rope with length L and mass m is held at one end and whirled in a horizontal circle with angular velocity omega. You can ignore the force of gravity on the rope. Find the time required for a transverse wave to travel from one end of the rope to the other.

So far by fiddling with some equations, I've got:

v = sqrt(F_tension/µ)

F_tension = ma = m*L*omega^2

µ = m/L

v = sqrt((m*L*omega^2)/(m/L)) = sqrt(omega^2*L^2) = omega*L

And of course, that gets me nowhere except another textbook equation, namely v = R*omega

So I have no idea where to go from there.

Any help will be appreciated.

2. Jan 19, 2005

### andye

Your equations look a bit fishy. For example, your last relation v=L*omega implies that the units of angular velocity are just meters, which isn't correct. Maybe you can relate L (angular momentum) in terms of distance L and linear density lambda and omega (or one of its derivatives?) by using the moment of inertia. Once we know the velocity, we already have the length, so the time it takes for a wave to travel down the rope's length should be easy. g'luck!