The Earth has an angular speed of 7.272·10 -5 rad/s in its rotation. Find the ne

Question

The Earth has an angular speed of 7.272·10-5 rad/s in its rotation. Find the new angular speed if an asteroid (m = 2.79·1022 kg) hits the Earth while traveling at a speed of 1.83·103 m/s (assume the asteroid is a point mass compared to the radius of the Earth) in each of the following cases:

a) The asteroid hits the Earth dead center.
7.1881×10-5 rad/s

b) The asteroid hits the Earth nearly tangentially in the direction of Earth's rotation.

c) The asteroid hits the Earth nearly tangentially in the direction opposite of Earth's rotation.

.

Explanation / Answer

part B :

apply the law of conservation of Angular momentum

Li = Lf

Ii 0 + R*m*V = If f

f = ((2M/5)*0 + mv/R)/(2M/5 + m)

Wf = ((2*(5.97e24)*(7.272e-5)/5) + ((2.79e22)*(1.83e3)/6371000))/((2*(5.97e24)/5) + (2.79e22))

Wf = 7.52 *10^-5 rad/s

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c) again Li = Lf

Ii 0 - R*m*V = If f

f = ((2M/5)*0 - mv/R)/(2M/5 + m)

Wf = ((2*(5.97e24)*(7.272e-5)/5) - ((2.79 e22)*(1.83e3)/6371000))/((2*(5.97e24)/5) + (2.79 e22))

Wf = 6.856 *10^-5 rad/s

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