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A child stands at the centre of a turnta...

A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value? Assume that the turntable rotates without friction.

Text Solution

Verified by Experts

Here, initial angular speed `omega_(1)=40` rev/min, `omega_(2)=?`
Final moment of inertia, `l_(2)=(2)/(5)I`, final moment of inertia
As no external torque acts in the process, therefore
I = constant
i.e. `I_(2)omega_(2)=I_(1)omega_(1)`
`omega_(2)=(I_(1))/(I_(2))omega_(1)=(5)/(2)xx40`
= 100 rpm.
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A child stands at the centre of a turn table with his two arms outstretched. The turn table is set rotating with an angular speed of 40 rpm. How much is the angular speed of the child, if he folds his hands back reducing the moment of inertia to (2/5) times the initial value? Assume that turntable rotates without friction.(b) Show that the child's new K.E of rotation is more than the initial K.E. of rotation. How do you account for this increase in K.E.?

A child stands at the centre of a turn table with his two arms outstretched. The turn table is set rotating with an angular speed of 40 rpm. How much is the angular speed of the child, if he folds his hands back reducing the moment of inertia to (2/5) times the initial value? Assume that turntable rotates without friction.(b) Show that the child's new K.E of rotation is more than the initial K.E. of rotation. How do you account for this increase in K.E.?

Knowledge Check

  • A man turns on rotating table with a omega angular speed. He is holding two equal masses at arms length. Without moving his arms, he hust drops the two masses. How will his angular speed change ?

    A
    less than `omega`
    B
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  • A man turns on rotating table with an angular speed omega . He is holding two equal masses at arms length. Without moving his arms, he just drops the two masses. How will his angular speed change ?

    A
    less than `omega`
    B
    more than `omega`
    C
    it will be equal to `omega`
    D
    it will be more than `omega` if the dropped mass is more than `9.8kg` and it will be less than `omega` if the mass dropped is less than `9.8kg`

  • A man turns on rotating table with an angular speed omega . He is holding two equal masses at arms length. Without moving his arms, he just drops the two masses. How will his angular speed change ?

    A
    less than `omega`
    B
    more than `omega`
    C
    it will be equal to `omega`
    D
    it will be more than `omega` if the dropped mass is more than 9.8 kg and it will be less than `omega` if the mass dropped is less than 9.8 kg

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