Question

A rod of mass `2kg` and length `1m` is pivoted at one end `A` and kept on a smooth surface. A particle of mass `500gm strikes the other end B` of the rod and sticks to the rod. If particle was moving with the speed of `20m//s`, what is the angular speed of the rod after collision ?

Answer 1

Since the rod is pivoted at point `A`, angular momentum of rod and particle system can only be conserved about the point `A`. Why ?
`L_(i)=m.v.r_(bot)=(1)/(2)xx10xx1=5kgm^(2)//s`
`L_(i)=I_(A)omega=((ML)/(3)+m.L^(2))omega=((2)/(3)+(1)/(2)xx1)omega=(7)/(6)omega`
`L_(i)=L_(f)implies5=(7)/(6)omegaimpliesomega=(30)/(7)=4(2)/(7)rad//s`