Ball and Stick

# Ball and Stick - The disc and stick A disc of mass 2 kg...

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The disc and stick A disc of mass 2 kg slides with velocity 3 m/s along a frictionless ice surface, and hits a stationary stick of total length 4 m and mass 1 kg. The impact is at right angles to the stick, exactly at one end. The impact is elastic, and, afterwards, the disc continues to move in its original direction. y t 3 m/s - 6 ? 4 m y t - u - U 6 ω Useful information: a stick of mass M and length 2 L has a moment of inertia about a perpendicular axis through its centre of I C = 1 3 ML 2 . For the present problem, this gives I C = 4 / 3 kg-m 2 . The problem is to find the velocity of the disc, u , and of the centre of mass of the stick, U , as well as the angular velocity ω of the stick around its centre of mass, all after the collision. Three unknowns. We use Conservation of momentum. Conservation of energy. Conservation of angular momentum about the CofM in the CofM frame. We will write down the first two conservation laws using the momentum and energy of the whole system, including the motion of the centre of mass. Since there are no external

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