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Find the angular speed of the Earth as it spins about its axis. Give your result in units of rad/s.

Feb 13th, 2015

Angular speed

The angular speed of Earth's rotation in inertial space is (7.2921150 ± 0.0000001) ×10−5 radians per SI second (mean solar second).[27] Multiplying by (180°/π radians)×(86,400 seconds/mean solar day) yields 360.9856°/mean solar day, indicating that Earth rotates more than 360° relative to the fixed stars in one solar day. Earth's movement along its nearly circular orbit while it is rotating once around its axis requires that Earth rotate slightly more than once relative to the fixed stars before the mean Sun can pass overhead again, even though it rotates only once (360°) relative to the mean Sun.[n 4] Multiplying the value in rad/s by Earth's equatorial radius of 6,378,137 m (WGS84 ellipsoid) (factors of 2π radians needed by both cancel) yields an equatorial speed of 465.1 m/s, 1,674.4 km/h or 1,040.4 mi/h.[32] Some sources state that Earth's equatorial speed is slightly less, or 1,669.8 km/h.[33] This is obtained by dividing Earth's equatorial circumference by 24 hours. However, the use of only one circumference unwittingly implies only one rotation in inertial space, so the corresponding time unit must be a sidereal hour. This is confirmed by multiplying by the number of sidereal days in one mean solar day, 1.002 737 909 350 795,[27] which yields the equatorial speed in mean solar hours given above of 1,674.4 km/h.

The tangential speed of Earth's rotation at a point on Earth can be approximated by multiplying the speed at the equator by the cosine of the latitude.[34] For example, the Kennedy Space Center is located at 28.59° North latitude, which yields a speed of: 1,674.4 kilometres per hour (1,040.4 mph) × cos (28.59) = 1,470.23 kilometres per hour (913.56 mph)

Reference Wikipedia

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