Thanks The Earth has an angular speed of 7.272.10-3 rad/s in its rotation. Find

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The Earth has an angular speed of 7.272.10-3 rad/s in its rotation. Find the new angular speed if an asteroid (m = 3.05.1022 kg) hits the Earth while traveling at a speed of 3.15.103 m/s (assume the asteroid is a point compared to the radius of the Earth) in each of the following cases: The asteroid hits the Earth dead center. The asteroid hits the Earth nearly tangentially in the direction of Earth's rotation. The asteroid hits the Earth nearly tangentially in the direction opposite of Earth's rotation.

Explanation / Answer

The speed of the Earth's rotation can be thought of in two ways - the angular speed and the linear speed (of a point on the surface). Express the angular speed (traditionally referred to by the Greek letter omega) in radians/sec: omega = 360 degrees / 24 hours = 2 * pi radians / (24 * 60 * 60) second (pi = 3.14159.....) = 7.272 x 10-5 radians/sec = 0.00007272 radians/second Now to convert the angular speed to the linear speed of a point on the Earth's surface, multiply omega by the radius of the Earth, R. To put it in familiar units, let's express R in miles: R = 3822 miles (roughly). So the linear velocity on the surface V is: V = omega * R = 0.00007272 * 3822 = 0.278 miles/second or V = about 1000 miles/hour (Surprisingly fast!)

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