Question

What is the work done in increasing the angular frequency of a circular ring of mass $2kg$ and radius $25cm$ from $10rpm$ to $20rpm$ about its axis?

• A. $0.15Joules$
• B. $0.18Joules$
• C. $0.2054Joules$
• D. $0.302Joules$

Answer 1

The correct option is C $0.2054Joules$

work done = change in rotational kinetic energy

$=\frac{1}{2}I(w_f^2-w_i^2)$

$=\frac{1}{2}M{R}^2(w_f^2-w_i^2)$

$=\frac{1}{2}\times 2\times (0.25{)}^2({\left(\frac{2\pi }{3}\right)}^2-{\left(\frac{\pi }{3}\right)}^2)$

$=0.2054J$