A particle of mass m, moving in a cicular path of radius R with a constant speed `v_2` is located at point (2R,0) at time `t=0` and a man starts moving with a velocity `v_1` along the +ve y-axis from origin at time `t=0`. Calculate the linear momentum of the particle w.r.t. the man as a function of time.

Answer

`-mv_(2) sin (v_(2))/(R ) t hat(i) + m (v_(2) "cos"(v_(2))/(R ) t - v_(1))hat(j)`

Explanation

`vec(v)_(2) = (-v_(2) sin omegathat(i) + v_(2) cos omegat hat(j))` and `vec(v)_(1) = v_(1) hat(j)`
`vec(v)_(21) = vec(v)_(2) - vec(v)_(1) = -v_(2) sinomegathat(i) + (v_(2) cos omega t - v_(1)) hat(j)`
`vec(p)_(21) = mvec(v)_(21) = -mv_(2) sin omegat hat(i) + m(v_(2) cos omegat - v_(1)) hat(j)`
where `omega = (v_(2))/(R )`