Gravity on a Rotating Body

## Question:

I'm debating someone regarding gravity.
I say Centrifugal force counters the effect of the earth's
gravitational pull and thus keeps us upright. Slow down the
earth's spin and gravity will squish us. Speed it up and we
fly off the earth.

My debate partner says no. Slowing down the earth will have no
affect on gravity. I say it won't have an affect on GRAVITY -
but it WILL have an affect on the FORCE of gravity. Gravity will
remain constant. But as the centrifugal force nears 0 we will
experience tremendous gravitation exertion and will probably fall
flat to the earth if not get squished.

My friend things I'm nuts. I think he is a moron. What do
you say?

Thank you kindly.

## Answer:

At the equator the effect of centrifugal force is maximum. At the
poles it is zero. Since we do not find polar bears or penguins
flattened by gravity, your friend seems to have a strong case.
Maybe what we should do is calculate the magnitude of the
centrifugal force due to our curved path as Earth turns and
compare that to the force of gravity at Earth's surface.
Let's take the radius of Earth to be 6.37 million meters.
Then the circumference is 2*p*6.37e6
or 40 million meters. At the equator we cover that distance in 24
hours as Earth turns so the tangential speed (Vt) of a person on
Earth's surface at the equator is 4e7/(24*3600) meters per
second. This comes out to be 463 meters per second.

Centrifugal force Fc is given by
Fc=m*Vt^{2}/R where m is the mass of the object at
Earth's surface and R is the radius of Earth. In our case
lets take the mass of a person to be 100kg so
Fc=100*463^{2}/6.37e6. That is
Fc=3.365 Newtons.

The force of gravity on this 100kg person is his mass times
the acceleration of gravity at Earth's surface. That is
9.8*100 or 9800 Newtons. Centrifugal force then reduces the force
holding the person to Earth's surface at the equator by about
0.034%.

Now we can address your argument. You are correct in theory
that centrifugal force reduces the effect of gravity. You are way
off in your assessment of the magnitude of this effect.