First slide

Rolling motion

Question

A disc of radius 2m 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?

Easy

A

2J
B

1J
C

3J
D

30KJ

Solution

Work required = change in kinetic energy
Final KE = 0
Initial $\large KE = \frac{1}{2}m{v^2} + \frac{1}{2}|{\omega ^2} = \frac{3}{4}m{v^2}$
$\large = \frac{3}{4} \times 100 \times {\left( {20 \times {{10}^{ - 2}}} \right)^2} = 3J;\;\left| {\Delta KE} \right| = 3\,J$

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