Question

A bird flies overhead from where you stand at an altitude of
280.0**ĵ** m and at a velocity horizontal to the
ground of 12.0**î** m/s. The bird has a mass of 2.4
kg. The radius vector to the bird makes an angle *θ* with
respect to the ground. The radius vector to the bird lies in the
*xy*-plane. What is the bird's angular momentum (in kg ·
m^{2}/s) about the point where you are standing? (Express
your answer in vector form.)

Answer #1

We know that Angular momentum is given by:

L = rxP

P = linear momentum = m*V

L = rx(m*V) = m*(rxV)

Now given that:

m = mass of bird = 2.4 kg

r = displacement vector suppose you're at origin = rf - ri = 280.0 j - (0 i + 0 j) = (280.0 j) m

V = Velocity of bird = (12.0 i) m/s

So,

L = 2.4*(280.0 j)x(12.0 i)

L = 2.4*280.0*12.0*(jxi)

In cross product: jxi = -k, So

L = 8064 (-k)

**L = Angular momentum = (-8064 k) kg.m^2/sec**

**Here -k means angular momentum is directed into the
ground**

Use +ve value only if you need magnitude

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