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Units And Measurement

Question
CBSEENPH11017663

Show that angular momentum of body revolving about an axis is twice the mass of arial velocity.

Solution
Let a particle of mass m be revolving in XY plane about Z axis.
           
Let, at any instant t particle be at A and at t + ∆t particle be at B.
Let the radius vector sweep the area ∆A in time ∆t. 
therefore space space space space capital delta A equals space A r e a space o f space straight capital delta space A O B
space space space space space space stack increment A with rightwards harpoon with barb upwards on top equals 1 half r with rightwards harpoon with barb upwards on top space cross times space stack increment r with rightwards harpoon with barb upwards on top
therefore space space A r i a l space v e l o c i t y comma space v with rightwards harpoon with barb upwards on top subscript a r end subscript space equals fraction numerator space space rightwards arrow for capital delta capital alpha of over denominator capital delta t end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 half fraction numerator rightwards arrow for straight r of cross times rightwards arrow for capital delta r of over denominator capital delta t end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 half rightwards arrow for straight r of cross times fraction numerator rightwards arrow for capital delta r of over denominator rightwards arrow for capital delta t of end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half r with rightwards harpoon with barb upwards on top cross times v with rightwards harpoon with barb upwards on top
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 half fraction numerator rightwards arrow for straight r of cross times straight m rightwards arrow for straight v of over denominator straight m end fraction space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator rightwards arrow for straight L of over denominator 2 straight m end fraction
therefore space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 2 straight m fraction numerator space space rightwards arrow for capital delta capital alpha of over denominator capital delta t end fraction