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physics

mechanics

Easy

Question

$A space c h i l d space i s space s tan d i n g space w i t h space h i s space t w o space a r m s space o u t s t r e t c h e d space a t space t h e space c e n t r e space o f space a space t u r n t a b l e space t h a t space i s space r o t a t i n g space a b o u t space i t s space c e n t r a l space a x i s space w i t h space a n space a n g u l a r space s p e e d space omega subscript 0 space. space N o w comma space t h e space c h i l d space f o l d s space h i s space h a n d s space b a c k space s o space t h a t space m o m e n t space o f space i n e r t i a space b e c o m e s space 3 space t i m e s space t h e space i n i t i a l space v a l u e. space T h e space n e w space a n g u l a r space s p e e d space i s$

$ω_{0}$
$\frac{ω_{0}}{3}$
$6 ω_{0}$
$\frac{ω_{0}}{6}$

The correct answer is: $\frac{ω_{0}}{3}$

$H e r e comma I n i t i a l space a n g u l a r space s p e e d space omega subscript i equals omega subscript 0 text Initial moment of inertia =I end text subscript i text end text text Final moment of inertia I end text subscript text f end text end subscript text end text equals 3 straight I subscript straight i straight L subscript straight i equals straight L subscript straight f straight I subscript straight i straight omega equals straight I subscript straight f straight omega subscript straight f straight omega subscript straight f equals fraction numerator straight I subscript straight i straight omega subscript straight i over denominator straight I subscript straight f end fraction equals open parentheses straight I subscript straight i over straight I subscript straight f close parentheses straight omega subscript straight i equals open parentheses fraction numerator straight I subscript straight i over denominator 3 straight I subscript straight i end fraction close parentheses straight omega subscript straight i open parentheses because straight I subscript straight f equals 3 straight I subscript straight i close parentheses equals straight omega subscript straight i over 3 equals straight omega subscript 0 over 3 open parentheses because straight omega subscript straight i equals straight omega subscript 0 close parentheses$

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