Question

Circular disc of mass 2 kg and radius 1 m is rotating about an axis perpendicular to its plane and passing through its centre of mass with a rotational kinetic energy of 8 J. The angular momentum in (J-s) is

• A. 8
• B. 4
• C. 2
• D. 1

Answer 1

Answer: (B)

4

Answer 2

Rotational kinetic energy $=\frac{1}{2}I{{\omega }^{2}}=8\,J$ $\Rightarrow$ $\frac{1}{2}\times \frac{1}{2}m{{r}^{2}}{{\omega }^{2}}=8$ or $\frac{1}{4}\times 2\times {{(1)}^{2}}{{\omega }^{2}}=8$ or ${{\omega }^{2}}=16$ or $\omega =4\,rad/s$ Angular momentum, $L=I\omega$ $=\frac{1}{2}m{{r}^{2}}\omega$ $=\frac{1}{2}\times 2\times {{(1)}^{2}}\times 4$ $=4\,J-s$