Question

Natalie is an accomplished ice skater with hopes of competing in the 2022 Winter Olympics in Beijing. One of her standard moves is to spin on point. She starts spinning at 3.5 rev/s with her arms outstretched and an associated moment of inertia I = 6.4 kg ∙ m². Natalie then brings her arms in and decreases her moment of inertia to I = 1.8 kg ∙ m². What is her final angular speed?

	A.	10 rev/s
	B.	3.5 rev/s
	C.	2.6 rev/s
	D.	12.4 rev/s

Answer 1

in this case angular momentum is conserved, therefore

$\frac{\omega _{2}}{\omega _{1}}=\frac{I_{1}}{I_{2}}$

Here, initial angular speed, $\omega _{1}=3.5rev/ sec$ ,

  $I_{1}=6.4kg.m^{2}$ amd  $I_{2}=1.8kg.m^{2}$

$\Rightarrow \omega _{2}=\frac{I_{1}}{I_{2}}\times \omega _{1}$

$\Rightarrow \omega _{2}=\frac{6.4}{1.8}\times 3.5=12.4rev/sec$

$\Rightarrow \omega _{2}=12.4rev/sec$

correct option is D part.