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Karol
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Homework Statement
A ball of mass m rotates without sliding at velocity v1 and hits a wall. it rotates backwards at velocity v2. what is the energy loss.
Homework Equations
Kinetic energy of a rigid body: ##E=\frac{1}{2}I\omega^2##
Moment of inertia of a ball round it's center: ##I=\frac{2}{5}mr^2##
3. The Attempt at a Solution
$$\Delta E=\frac{1}{2}m(v_2^2-v_1^2)+\frac{1}{2}I(\omega^2_2-\omega^2_1)$$
$$\omega r=v\rightarrow \omega^2=\frac{v^2}{r^2}$$
$$\Delta E=\frac{1}{2}m(v_2^2-v_1^2)+\frac{1}{2}\frac{2}{5}mr^2\cdot\left( \frac{v_2^2-v_1^2}{r^2} \right)$$
$$\Delta E=\frac{1}{2}m(v_2^2-v_1^2)\left( 1+\frac{2}{5} \right)$$
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