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  4. The kinetic energy of a circular disc rotating with a speed of 60 r.p.m. about an axis passing through a point on its circumference and perpendicular to its plane is (mass of circular disc =5 kg, radius of operatornamedisc=1 m ) approximately.

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Q. The kinetic energy of a circular disc rotating with a speed of $60$ r.p.m. about an axis passing through a point on its circumference and perpendicular to its plane is (mass of circular disc $=5\, kg$, radius of $\operatorname{disc}=1 \,m$ ) approximately.

AP EAMCETAP EAMCET 2015

Solution:

The rotational kinetic energy is given by
$KE =\frac{1}{2} I \omega^{2}=\frac{1}{2} \times \frac{3}{2} mr ^{2} 4 \pi^{2} f^{2}$
where, $m=$ mass, $r=$ radius and $f=$ frequency
$\Rightarrow KE =3\, mr ^{2} \times \pi^{2} f ^{2}=3 \times 5 \times 1 \times 10 \times 1$
$\Rightarrow KE =150 \,J$