How long would it take to stop the rotation of the Earth?

[Vodkacannon]

Imagine a person is moving at the equator in the direction opposite of the Earth's spin. How long would it take them to stop the rotation of the Earth?

Assume:

the person's "weight" = 90.718 kg,

they person's speed = 1m/s,

The Earth's "weight" = 5.972*10^24 kg,

the angular velocity of the Earth = 7.292*10^-7 rad/s,

The radius of the Earth = 6.371*10^6 m,

and the inertia of the Earth = 8*10^37 kgm^2

 

[willem2]

Imagine a person is moving at the equator in the direction opposite of the Earth's spin. How long would it take them to stop the rotation of the Earth?

Such a person won't stop the rotation of the Earth at all. The angular momentum of the Earth is conserved. The Earth can only lose angular momentum by interacting with another object and transfering the angular momentum to it. Obviously this person can take only a tiny bit of the Earth's angular momentum without flying up into space (or burning up in the atmosphere).
While the person is walking around the equator at constant speed, his or her angular momentum doesn't change at all, and neither does the angular momentum of the Earth.

 

[Fig Neutron]

Wouldn’t the person also have to be moving in the same direction the Earth is spinning? That way as he walked he would be pushing the opposite direction the Earth is turning.

 

[willem2]

Wouldn’t the person also have to be moving in the same direction the Earth is spinning? That way as he walked he would be pushing the opposite direction the Earth is turning.

The direction doesn't matter. If you walk with a constant speed, you won't push the earth, and it won't push you. Any friction force needed to move forward will be canceled by the effects of air resistance. There's no way to change the angular momentum of the Earth without an external force.
Of course the moon can do it: https://en.wikipedia.org/wiki/Tidal_acceleration

 

[CWatters]

There would only be a torque slowing the Earth while you are accelerating. You would have to go faster and faster until your angular momentum was the same as the Earth had originally. Then the Earth would be stationary while you "run" exceptionally fast.

How fast? Well way before you are going fast enough the centripetal force required to stay in contact with the ground would exceed the force of gravity and you would lift off the ground.

Ok so to fix that you could build some sort of track around the equator to attach yourself to and provide the necessary centripetal force to hold you down.

I haven't done the sums but I suspect you would still have to go exceptionally fast. Probably faster than the speed of light - which is impossible.

Edit: There would be a bunch of other problems.

 

[jbriggs444]

Probably faster than the speed of light - which is impossible.

Certainly fast enough that momentum and angular momentum are no longer linear functions of velocity and asymptotically increase without bound as the speed of light is approached. Fast enough that the track not only has to be inverted, but evacuated. Fast enough that the runner's energy would dramatically exceed the original rotational energy of the Earth. Fast enough that the centrifugal stress on the track would exceed any reasonable material strength. Fast enough that the centrifugal force in the rotation rate of the runner's body in its orbit around the Earth would tear him limb from limb (though he'd hardly notice, being jellified into the track surface first).

 

[CWatters]

So just a few minor details to solve :-)