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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.