Dumbbells Collision: Work Out Centre of Mass & Angular Velocity

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The discussion focuses on a collision scenario involving two identical dumbbells treated as point masses connected by a weightless rod. The initial velocities of the dumbbells are given, and the problem requires calculating the center of mass velocity and angular velocity post-collision, considering the coefficient of restitution. Participants emphasize the importance of conserving momentum and angular momentum during the collision, while noting that the energy equation must be adjusted for inelastic collisions. The coefficient of restitution plays a crucial role in determining how kinetic energy is affected during the collision. Understanding these principles is essential for solving the problem accurately.
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Two identical dumb-bells are placed so that their ends are at (−d, +2l), (−d, 0), and (+d, 0), (+d,−2l). Each can be considered as two point masses m joined by a weightless rod of length 2l. Initially they are not rotating, and move with velocities (+V,0), (-V,0) so that the top of one hits the bottom of the other. If the coefficient of resitution is e then work out the centre of mass velocity and the angular velocity of each rod after the collision.

I tried doing this by energy and angular momentum conservation, which I think I can do if it's an elastic collision, but I'm not sure how the coefficient of restitution affects that. Any help would be greatly appreciated.
 
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jsmith12 said:
I tried doing this by energy and angular momentum conservation, which I think I can do if it's an elastic collision, but I'm not sure how the coefficient of restitution affects that.

Hi jsmith12! :smile:

(When in doubt, try wikipedia … http://en.wikipedia.org/wiki/Coefficient_of_restitution)

In collisions, momentum and angular momentum are always conserved … so it's only the energy equation you have to change when the collision isn't elastic! :smile:
 

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