# Lecture 903, Slide 9: Two Identical pucks pulled by strings

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Strings are wound around two identical pucks: puck 1 around its outer rim (larger radius); the puck 2 around its axle (smaller radius). If both are pulled from rest with the same force F across a frictionless surface, which puck has greater center-of-mass speed?

The answer is both have the same C.O.M speed. I am trying to understand why. Am I right in saying the following?

Puck 2 will have a greater rotational speed do to its smaller radius. However, since most of the force applied goes into the rotational speed, it has less translational speed. The opposite is true for Puck 1. Somehow they end up with the same CoM speed.

Am I right? Is there an equation I'm missing/forgetting?

When dealing with both rotational and translational motion, we need to separate the two. For translational motion, $ma=F_{net}$ and for rotational motion $\alpha=I\tau$.