How much torque would be needed to stop the Earth from rotating on its axis?

Answer 1

that would depend on how long a time you took to bring the Earth's rotation to a halt

Torques create changes in angular velocity according to:

Torque = moment of inertia x angular acceleration

the moment of inertia is a measure of an object's resistance to changes in rotational motion, the angular acceleration is the rate of change of angular velocity

the moment of inertia of the Earth (assuming it as a sphere) is 0.4MR^2 where M is the Earth/s mass and R its radius.

the angular velocity of the Earth is 2 Pi/86,400 s, and this is the amount of angular velocity change you need to bring the rotation to zero

the torque needed to halt the earth's rotation is then:

torque=0.4MR^2*(2Pi/86,400)/t
where t is the time in which you want to accomplish this...plug in values and it's all there

Answer 2

You need to be more specific as to how quickly you want to stop the Earth. Any amount of torque will stop the Earth's rotation if it's applied long enough.

For example, the Moon applies a torque of 1.46 x 10^16 Nm on the Earth. At that torque, it will take about 15.4 billion years for the Moon to stop the Earth's rotation. That's a bad example, since the Moon is actually orbiting the Earth, so the Moon can't slow the Earth down below the Moon's angular velocity around the Earth, but it gives an idea of how huge a torque you would need to stop the Earth. (It's also a bad example since the oceans will boil away in around 2.1 billion years, eliminating the source of the Moon's torque on Earth.)

Re: Kevin's response. There would be no torque if the Earth were a perfect sphere. The Moon's gravity creates bulges (the tides) that would align with the Moon's radius IF the Earth's rotational angular velocity matched the Moon's orbital angular velocity. Since the Earth is rotating once every 1436 minutes and the Moon takes nearly a month to orbit, the Earth's rotation pulls the tides with it, meaning the Moon is never successful in aligning the tides with the Moon's radius.

Answer 3

Since the earth is rotating through its magnetic field which is about half a gauss or 0.5E-4 Teslas
Its torque is given by
t = I *A *B
where I = current in amps
B = magnetic field in T
and A = the area it is working over
so if you want to stop that
I*A*B = 2/5mr^2*ω= F*l
it depends on what you want to do. Either use a huge lever or run a tremendously large current through it.

Answer 4

Time derivative related misconceptions are very common in intro physics. A given torque with result in a given time rate of change of angular velocity, so it all depends on how patient you are. Torque from tidal drag from the moon slows the earth's rotation significantly over billions of years.

Answer 5

Literally any nonzero torque is enough, provided that you apply the torque for a sufficiently long time.

The formula is:

τ = Iω / T

Where:
τ = the torque
I = earth's moment of inertia (about 8 × 10^37 kg-m², according to this website: http://scienceworld.wolfram.com/physics/MomentofInertiaEarth.html )
ω = earth's angular velocity (7.3 × 10^-5 rad/sec)
T = time period over which you apply the torque.

For example, let's say you wanted the earth to stop after 1 hour of torque. In that case:

τ = (8 × 10^37 kg-m²)(7.3 × 10^-5 rad/sec) / (3600 s)
= 4.0 × 10^29 N-m

Answer 6

Actually, Bob G,

The moon does not, in fact have any torque on the Earth, as by definition, torque is Force X Distance. The force of the moon on the earth is the same directional vector as the distance. When you cross two vectors of the same direction, your cross product is zero.

Answer 7

You need to look up the length of the lever arm of earth. This would be equal to the radius of the earth. Half the diameter. Then you would need to use a torque equation from physics one to calculate the torque. Hope this helps.