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  4. A circular disc has a mass of 1 kg and radius 40 cm . It is rotating about an axis passing through its centre and perpendicular to its plane with speed of 10 rev / s. The work done in joules in stopping it would be (π2 ≈ 10) :

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Q. A circular disc has a mass of $1 \,kg$ and radius $40 \,cm .$ It is rotating about an axis passing through its centre and perpendicular to its plane with speed of $10 rev / s$. The work done in joules in stopping it would be $\left(\pi^{2} \approx 10\right)$ :

System of Particles and Rotational Motion

Solution:

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$W =\Delta K$
$W =\frac{1}{2} I \omega^{2}$
$=\frac{1}{2} \frac{ MR ^{2}}{2} \times(2 \pi f )^{2}$
$=\frac{M R^{2}}{4} \times 4 \pi^{2} \times(10)^{2}$
$=1 \times(0.4)^{2} \times 10 \times 100$
$\simeq 160$