Question

A ring of mass $10kg$ and diameter $0.4$ meter is rotating about its geometrical axis at $2100$ rotations per minute. Its moment of inertia and angular momentum will be respectively:

• A. $0.4{kg-m}^2$ and $88$ Joule-sec
• B. $0.4{kg-m}^2$ and $0.4$ Joule-sec
• C. $50.28{kg-m}^2$ and $0.4$ Joule-sec
• D. $0.4{kg-m}^2$ and $zero$

Answer 1

The correct option is A $0.4{kg-m}^2$ and $88$ Joule-sec

Radius of ring, $R=0.4/2=0.2m$

Mass of ring, $M=10kg$

(i)Moment of inertia

$I=M{R}^2$

$I=10\times (0.2{)}^2$

$I=0.4kg-m^2$

(ii)Angular momentum

$L=I\omega$

$\omega =2\pi \nu$

$\nu =2100rpm=2100/60rps$

$L=0.4\times 2\pi \times 2100/60$

$L=87.93\approx 88joule-sec$