Question

A particle executes uniform circular motion with angular momentum 'L'. Its rotational kinetic energy becomes half when the angular frequency is doubled. Its new angular momentum is ______.

Options

• 4L

• `L/4`

• 2L

• `L/2`

Answer 1

A particle executes uniform circular motion with angular momentum 'L'. Its rotational kinetic energy becomes half when the angular frequency is doubled. Its new angular momentum is `underline(L/4)`.

Explanation:

`K=1/2Iomega^2,`      L = Iω

`K^'=1/2I^'omega'^2,`    ω' = 2ω

`thereforeK^'=1/2I^'(2omega)^2,  K^'=K/2`

`therefore1/2(1/2Iomega^2)=1/2I^'(2omega)^2`

`thereforeI^'=1/8`

`L^'=I^'omega^'=1/8xx2omega=(Iomega)/4=L/4`