A ball of mass m falls down without initial velocity from a height h over the Earth's surface. Find the increment of the ball's angular momentum vector picked up during the time of falling (relative to the point O of the reference frame moving translationally in a horizontal direction with a velocity V). The ball starts falling from the point O. The air drag is to be neglected.

Explanation

During the free fall time `t=tau=sqrt((2h)/(g))`, the reference point O moves in horizontal direction (say towards right) by the distance `V tau`. In the translating frame as `vecM(O)=0`, so
`DeltavecM=vecM_f=vecr`
`=(-V tau veci+h vec j)xxm[gt auvecj-V vecj]`
`=-mVg tau^2vech+mVh(+veck)`
`=-mVg((2h)/(g))veck+mVh(+veck)=-mVh veck`
Hence `|Delta vecM|=mVh`