(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

w = θ/time

α = w^{2}r = centripetal acceleration

α = g

g = w^{2}r = acceleration due to gravity

r = g/w^{2}

3. The attempt at a solution

Since α has the values m s^{-2}and g = m s^{-2}

α = g

if

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 = w^{2}r

to

r = g/w^{2}

= 9.81/(7.272 * 10^{-5})^{2}m

≈1.86 * 10^{9}m

Now if I google radius of earth I get 6.37 * 10^{6}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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# Homework Help: Linking gravity, angular velocity and radius

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