- #1
jonnybmac
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Homework Statement
I am having trouble linking gravity to the radius of the Earth and angular velocity. I was using this as a solid method to confirm the equation for values of a different sort based on centripetal acceleration. When inputting the values though it does not add up and I cannot see where and why
Homework Equations
w = θ/time
α = w2r = centripetal acceleration
α = g
g = w2r = acceleration due to gravity
r = g/w2
The Attempt at a Solution
Since α has the values m s-2 and g = m s-2
α = gif
w = 2π/86400 (rotation of Earth per day)
≈ 7.272 * 10-5 rad s-1
and
g = 9.81 m s-2
then aranging
g = w2r
to
r = g/w2
= 9.81/(7.272 * 10-5)2 m
≈1.86 * 109 m
Now if I google radius of Earth I get 6.37 * 106 m
This is nowhere near the radius that I should be getting with the above equation, so where am I going wrong?
Many thanks for reading
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