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Two point masses, with masses of m and 2m, are connected through a string that has a length of L. The two bodies are put on an horizontal frictionless table as in the figure, so that m is at the origin. The body 2m is above it (on the y axis) at a distance of L/2 m. At a certain moment they give 2m a velocity of v0 in the positive x axis direction.

What's the kinetic energy of the system after the string is streched and m starts to move?

I realize that conservation of both linear and angular momentum applies here - but I don't understand something: Am I suppose to understand that the system starts to rotate about an axis which passes through the center of mass just as the string is streched? And if so - was there any "mathmatical way" for me to know the system starts rotating? Because it seems from the solution that when they calculated the angular momentum of the system as the string was streched - they used Icm*w to describe its angular momentum, while when they calculated the angular momentum of the system at the beginning (The picture phase) they used L=mvrsin(q) to describe the angular momentum as the sum of the angular momentum of 2m and m with respect to the center of mass...

What's the kinetic energy of the system after the string is streched and m starts to move?

I realize that conservation of both linear and angular momentum applies here - but I don't understand something: Am I suppose to understand that the system starts to rotate about an axis which passes through the center of mass just as the string is streched? And if so - was there any "mathmatical way" for me to know the system starts rotating? Because it seems from the solution that when they calculated the angular momentum of the system as the string was streched - they used Icm*w to describe its angular momentum, while when they calculated the angular momentum of the system at the beginning (The picture phase) they used L=mvrsin(q) to describe the angular momentum as the sum of the angular momentum of 2m and m with respect to the center of mass...

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