Centrifugal Force and Gravity

## Question:

Date: Thursday, February 10, 2000 1:15 PM
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:

Really a neat question. 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*pi*6.37e6 or 40 million meters. We cover that distance
in 24 hours as Earth turns so the tangential speed (Vt) of a person on
Earth's surface 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 980 Newtons.
Centrifugal force then reduces the force holding the person to Earth's
surface by about 0.34%.

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.

JDJ