A-small-particle-of-mass-m-is-projected-at-an-angle-with-the-x-axis-with-an-initial-velocity-v-0-in-the-x-y-plane-as-shown-in-the-Figure-At-a-time-t-lt-v-0-sin-g-the-angular-momentum-of-

Question Number 20375 by Tinkutara last updated on 26/Aug/17

A small particle of mass m is projected

at an angle θ with the x - axis with an

initial velocity v_{0} in the x - y plane as

shown in the Figure . At a time

t < \frac{v_{0} \sin θ}{g}, the angular momentum of

the particle is

Commented by Tinkutara last updated on 26/Aug/17

Answered by ajfour last updated on 26/Aug/17

\bar{L} = \int_{0}^{t} (x \hat{i} + y \hat{j}) \times (- m g \hat{j}) d t

= - \int_{0}^{t} [(v_{0} \cos θ) (m g) \hat{k}] t d t

= - ({m g v}_{0} \cos θ) \frac{t^{2}}{2} \hat{k}

∣ \bar{L} ∣= \frac{1}{2} ({m g v}_{0} \cos θ) t^{2} .

Commented by Tinkutara last updated on 26/Aug/17

Thank you very much Sir!