A particle of mass m moves in a generalized plane with fixed

A particle of mass m moves in a generalized plane with fixed unit vectors ere: with a position vector given by r vector = a cos(omega t)e_1 unit vector +asin(omega t)e_2 unit vector where omega is a constant. Show that the particle\'s velocity v vector is orthogonal to r vector. Find the particle\'s angular momentum L vector = r vector times m v vector. You will have to introduce a third unit vectors, orthogonal to e_1 unit vector and e_2 unit vector.

Solution

We know that when two vectors are orthogonal

There dot product is zero, hence

v.r =0

v = Dr/dt

v = -a sin (wt) + a cos ( wt)

Hence we can showthat

v .r = a^2 sin cos -   a^2 sin cos =0