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Suppose there are two congruent disks that are both rotating on its center axis but in opposite directions. A stationary ball is fed in between the two disks, where it collides with both disks and experiences an acceleration outwards.(This is exactly how automatic Nerf guns work). In what ways would they interact? Is there a general equation that explains this? How does the angular velocity of the two disks translate into the linear velocity of the ball? Thanks.

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Nevermind I got it! I considered the ball as a point mass that was rotating around the circumference of one of the disks as its final angular momentum. I saw the question as a reverse situation of a figure skater changing from skating linearly to rotating around a pole.

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Well I think what you wanted to ask is how a ball at rest suddenly gains velocity when it comes in contact with the two oppositely rotating discs. The discs have a w(omega) since they are rotating the tangential velocity at any point on a rotating disc or a body performing a circular motion is given by v=rw[ r=distance from the centre of rotation, w=omega of the disc ] considering the w of both the discs to be constant and equal, the ball will be impacted by the tangential velocities of both the discs simultaneously( hence providing it with an impulse in (dt)time ) Hence rw+rw =2rw the velocity aquired by the ball after coming in impact with the discs enter image description here

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