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A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?
Detailed Solution
Work required = change in kinetic energy; final KE = 0.
For a rolling disc: $KE_i=\frac{1}{2}mv^2+\frac{1}{2}I\omega^2=\frac{1}{2}mv^2+\frac{1}{2}\cdot\frac{1}{2}mr^2\cdot\frac{v^2}{r^2}=\frac{3}{4}mv^2$
$KE_i=\frac{3}{4}\times100\times(20\times10^{-2})^2=3\ J$
$|\Delta KE|=3\ J$