Question

If the radius of earth shrinks by $0.2\%$ without any change in its mass, its angular velocity:

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

Answer 1

The correct option is A increases by $0.4\%$

$R^{\prime }=R(1-0.002)$

Using conservation of angular momentum

$\frac{2}{5}M{R}^2{\omega }_i=\frac{2}{5}M{R}^2(1-0.002{)}^2{\omega }_f$

${\omega }_i={\omega }_f(1-0.002{)}^2$

${\omega }_f={\omega }_i(1-0.002{)}^{-2}$

${\omega }_f={\omega }_i(1+0.004)$

i.e. $w_f$ is increased by $0.4$%

We used $(1+a{)}^{-n}=1-an$

if $a\ll 1$