A particle of mass, initially at the origin<0,0,0>, is shot into the air with an

Question

A particle of mass, initially at the origin<0,0,0>, is shot into the air with an initial velocity v=<vocos?,0,vosin ?>,i.e. at a speed vo and making an angle ? with the horizontal. The particle moves in the graviational field of the Earth. You may neglect friction.

a). find the position and velocity vectors of the particle as a function of time. USing these vectors, determine the angular momentum L=r x p of the particle about the origin when it is at 1). at the orgin. 2). at the highest point of its trajectory/ and 3). just before it hits the ground

b). What torque causes the angular momentum to change.Repeat your calculation of 2) and 3) above by solving the equation of motion for the angular momentum.

Explanation / Answer

I will tell you the procedure and concept

a)

position vector s = ucos(theta)t i + (1/2 g t^2 ) j

velocity vector v = ucos(theta)t i + u sin(theta) j

angulat moemntum is given by

L= m (s * v) do the cross product of the above two vectors you get angular momentuma at any time interms of theta substitute theta asfor different positions you get all the answers for the first part

b)

use torque = dL/dt this is one of the elementary equations in rotatory dynamics you get the second answer

feel free to comment if you have any doubts

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