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The angular velocity of the tree on the equator can be calculated using the formula:
Angular velocity (ω) = 2π / T
Where T is the time it takes for the earth to complete one full rotation. Since the earth completes one full rotation in one day (24 hours), T = 24 hours.
Now we convert the time to seconds:
24 hours x 60 minutes/hour x 60 seconds/minute = 86,400 seconds
Now we can calculate the angular velocity:
ω = 2π / 86,400 seconds
ω ≈ 7.27 x 10^-5 rad/s
Therefore, the angular velocity of the tree on the equator is approximately 7.27 x 10^-5 radians per second.