A particle performs uniform circular motion with an angular momentum L. If the frequency of particle’s motion is doubled and its kinetic energy is halved, the angular momentum becomes

Engineering

Physics

Conservation of Angular Momentum

Question

L/2

L/4

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$\frac{I_{1} ω_{1}}{I_{2} ω_{2}}$ = $\frac{L_{1}}{L_{2}}$
ω₂ = 2ω₁
$\frac{1}{2}$ I₂ω₂² = $\frac{1}{2} (\frac{1}{2} I_{1} ω_{1}^{2})$ ⟹ I₂ = $\frac{I_{1}}{8}$
⟹ L₂ = $\frac{L_{1}}{4}$

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