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p = mv

L = Iω

These correspond to linear and angular momentum, respectively. They're both called momentum, but...they don't have the same units. Why is that?? How can we call them both momentum when they don't seem to represent the same physical quality? Can we set up equations of momentum conservation when going from a system of linear motion to one of rotational motion, like a sticky clay ball thrown in the air onto the edge of a rotating disk? If so, how do we account for this difference in the definitions of linear and angular momentum?