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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?

1. 3 J
2. 30 kJ
3. 2 J
4. 1 J

Correct answer: 3 J

Solution

The total kinetic energy of the rolling disc is the sum of its translational and rotational kinetic energies. Translational KE = (1/2)mv² = (1/2)(100)(0.2)² = 2 J. Rotational KE = (1/2)Iω², where I = (1/2)MR² for a disc and ω = v/R. Substituting, Rotational KE = (1/2)(1/2)(100)(2)²(0.2/2)² = 1 J. Total KE = 2 J + 1 J = 3 J. Thus, 3 J of work is needed to stop the disc.

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