A particle of mass m, moving in a circular 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_0` along the positive y-axis from origin at time t = 0. Calculate the linear momentum of the particle w.r.t. man as a function of time ______________.

Answer

`m[(-v_2 sin ((v_2)/(R )t)) hati + (v_2 cos ((v_2)/R t) - v_1) hatj]`

Explanation

Angular speed of particle about centre of the circle `omega = (v_2)/(R )`
Angle rotated by particle `theta = omegat = (v_2)/R t`
Velocity of the particle `vecv_p = (-v_2 sin theta hati + v_2 cos theta hatj)`
`vecv_P = (-v_2 sin ((v_2)/R t) hatj)`
and velocity of man `vecv_("man") = v_1 hatj`
`:.` Linear momentum of particle w.r.t man as a function of time is
`vecP_("particle, man") = m(vecv_("particle") - vecv_("man")) = m [(-v_2 sin ((V_2)/R t)) hati + (v_2 cos ((v_1)/(R) t) - v_1) hatj]`