Question

A metallic circular wheel is rotating about its own axis without friction. If the radius of wheel expands by $0.2\%$, percentage change in its angular velocity is:

• A. increases by $0.1\%$
• B. decreases by $0.1\%$
• C. increases by $0.4\%$
• D. decreases by $0.4\%$

Answer 1

Answer: (D)

decreases by $0.4\%$

Let the initial radius be r and final is $r_2=1.002r$

Now using the angular momentum conservation

$I_1{\omega }_1=I_2{\omega }_2$

We get $m{r}^2\times {\omega }_1=m{r}_2^2\times {\omega }_2$

So $\frac{{\omega }_1}{{\omega }_2}=\frac{(1002{)}^2}{{1000}^2}=1.004$

So Decrease in $\omega =0.004or0.4$%