Find the angular momentum about the axis of rotation and kinetic energy.
(a) A uniform circular disc of mass `m` and radius `R` rotating about its diameter with an angular speed `omega`.
(b) A uniform square plate of mass `m` and edge `L` rotating about its diagonal with an angular speed `omega`.

Explanation

The `M.I.` of the cirular disc about its diameter
`I=(1)/(4)mR^(2)`
The `M.I.` of the square plate about its diagonal `I=(mL^(2))/(12)`
(`a`) Angular momentum `L=Iomega=(1)/(4)mR^(2)omega`
Kinetic energy `K=(1)/(2)Iomega^(2)=(1)/(2)xx(1)/(4)mR^(2)omega^(2)=(1)/(8)mR^(2)omega^(2)`
(`b`) `L=Iomega=(mL^(2))/(12)omega`
`K=(1)/(2)Iomega^(2)=(1)/(2)(mL^(2))/(12)omega^(2)=(1)/(24)mL^(2)omega^(2)`