Question

A projectile of mass m is launched with an initial velocity v_i making an angle θ with the horizontal as shown below. The projectile moves in the gravitational field of the Earth. Find the angular momentum of the projectile about the origin when the particle is at the following locations. (Use the following as necessary: vi, θ, m, and g for the acceleration due to gravity.)
Find L at the highest point and right before it hits the ground

Answer 1

L at highest point =m*vcos(θ)*max hight=mvcosθ *{v^2 sin^2(θ)/2g}

Answer 2

it says that is incorrect

Answer 3

You want the angular momentum of the ball? We need the angular velocity, and I see now way to calculate that with the information given.

Answer 4

@quarkine i believe what is asked is the L around the origin of the projectile, so L of the mass m around the launching point, so you need to know the distance between the origing and the mass m.

Answer 5

@quarkine
so for at hmax:

\[L = I.\omega = m.r ^{2}.\omega = m.r ^{2}.r.v = m.r ^{3}.v\]
where v the component perpendicular to the radius
i get with
\[r = \frac{v _{i}^{2} . \sin ^{2} \theta}{2.g}\]
L at max height:
\[L = \frac{m.v _{i}^{7}.\sin ^{6}\theta.\cos \theta}{8.g ^{3}}\]