How Does a Pendulum on a Rotating Arm Behave When the Arm Stops?

[volican]

Scenario

There is a pendulum suspended on an arm that rotates a certain angle in the horizontal plane. The arm suddenly stops, how far will the mass of the pendulum be displaced in the horizontaly?

Thought so far:

The momentum of the arm will be L=IW and when it stops I think the mass at the end of the rope will have this amount of momentum. I know that momentum is conservative, is it valid to equate angular momentum to linear momentum. If so, knowing the momentum of the suspended mass how could I work out how this would translate to horizonal displacement?

Is my thinking ok or am I off. Any help or advice would be much appreciated.

 

[BvU]

Is my thinking ok or am I off

Yes and yes, in that order.
If you don't tell us what L, I or W is your account is hard to follow. I suspect dimensional errors in your thinking:

is it valid to equate angular momentum to linear momentum

No, they have different dimensions.

The problem statement is, anyway, incomplete: you do not mention any initial conditions at all.

[edit] This question fits very well in the context of your other threads. My advice would be to try and re-write your post #1 into a complete example problem statement using the template:

Homework Statement

include initial conditions. These can be general (difficult) or very simple -- so simple this whole problem amounts to having initial conditions for a spherical pendulum and you can forget about the boom altogether
​

Homework Equations

The Attempt at a Solution

and then work it out with the Euler-Lagrange formalism