Linear Tone
Posted February 14, 2009
By admin
Velocity of a mixer blade?
assuming the radius of the earth is 4,000 miles, and the eath rotates through one complete revolution every 24 hours. since the axis of rotation is perpendicular to the equatior, you can think of a person standing on the equator as standing on the edge of a disc that is rotationg throuhg tone complete revolution every 24 hours. Find the linear velocity of a person standing on the equator?
Using the assumptions given, the angular velocity w is 2π rad / 24 hr = (2π rad / 24 hr)(1 hr / 3600 s) = 0.0073 rad/s. The linear velocity at a distance r from the axis of rotation is v = rw = (4000 mi)(0.0073 rad/s) = 0.29 mi/s. If you prefer, that's (0.29 mi/s)(3600 s / 1 hr) = 1047 mi/hr.
If you look up the real value, it's 465.11 m/s. 0.29 mi/s is equal to 468 m/s, so our answer appears to be correct, modulo the assumptions regarding the Earth's diameter and rotation speed.
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