Question

A child is standing with his two arms outstretched at the centre of a turntable that is rotating about its central axis with an angular speed . Now, the child folds his hands back so that moment of inertia becomes 3 times the initial value. The new angular speed is

• A. 3 $\omega _ { 0 }$
• B. $\frac { \omega _ { 0 } } { 3 }$
• C. $6 \omega _ { 0 }$
• D. $\frac { \omega _ { 0 } } { 6 }$

Answer 1

Answer: (B)

$\frac { \omega _ { 0 } } { 3 }$

Answer 2

Here, Initial angular speed,

Initial moment of inertia, =

Final moment of inertia, $I _ { f } = 3 I _ { i }$

According to the law of conservation of angular momentum, we get,

$\mathrm { L } _ { \mathrm { i } } = \mathrm { L } _ { \mathrm { f } }$

$\omega _ { f } = \frac { I _ { i } \omega _ { i } } { I _ { f } } = \left( \frac { I _ { i } } { I _ { f } } \right) \omega _ { i } = \left( \frac { I _ { i } } { 3 I _ { i } } \right) \omega _ { i }$ ( )

$= \frac { \omega _ { i } } { 3 } = \frac { \omega _ { 0 } } { 3 }$