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The Earth's radius is 6371 km and its mass is 5. 97×10²⁴ kg. The following questions are about the Earth's rotaiton around its own axis, NOT its orbit around the sun. Assume the Earth is spherical. What is the Earth's angular velocity in rad/s?

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Answer: To find the Earth's angular velocity in rad/s, we need to know the time taken for one complete rotation (period) of the Earth around its own axis.

The formula for angular velocity (ω) is given by:

ω = 2π / T

where:

ω = angular velocity in rad/s

T = period of rotation in seconds

The period of rotation is the time taken for the Earth to complete one full rotation, which is approximately 24 hours (86,400 seconds) for a sidereal day. A sidereal day is the time taken for the Earth to rotate 360 degrees with respect to the stars.

Now, let's calculate the Earth's angular velocity:

ω = 2π / T

ω = 2π / 86,400 s

ω ≈ 7.27 × 10^(-5) rad/s

The Earth's angular velocity around its own axis is approximately 7.27 × 10^(-5) rad/s.

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