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  • Help me solve this! A particle performing uniform circular motion has angular momentum L . its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

A particle performing uniform circular motion has  angular momentum L . its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

Option 1)

L/4

 Option 2)

2L
Option 3)

4L

 Option 4)

L/2

Answers (1)

best_answer

As we learnt in

Rotational angular momentum -

\vec{L}= I\vec{w}

 

- wherein

I = Moment of inertia about fixed axis of rotation

w = angular velocity of rotation

 

 

 We know that L=I\omega

K.E_{not}=\frac{1}{2}I \omega^{2} 

\frac{L}{K}_{not}=\frac{2I\omega}{I\omega^{2}}=>\frac{L}{K}=\frac{2}{\omega}=>L=\frac{2K}{\omega}

\therefore \frac{L_{1}}{L_{2}}=\frac{K_{1}}{K_{2}}\times \frac{\omega_{2}}{\omega_{1}}=2\times 2=4

    \frac{L_{1}}{L_{2}}=4=>L_{2}=\frac{L_{1}}{4} = \frac{L}{4}


Option 1)

L/4

This is the correct option.

Option 2)

2L

This is an incorrect option.

Option 3)

4L

This is an incorrect option.

Option 4)

L/2

This is an incorrect option.

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Aadil

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