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I understand that the earth continues to rotate about its axis because the angular momentum is conserved. (Am i wrong?!) But, I have seen quite a few sources cite that inertia is the reason why the earth keeps spinning.

1.Veritasium

2.Universe Today

The Earth spins because it formed in the accretion disk of a cloud of hydrogen that collapsed down from mutual gravity and needed to conserve its angular momentum. It continues to spin because of inertia.

Is this really true? I always thought of inertia as the tendency of a body to continue moving along a straight line with a constant velocity (which maybe zero). Can someone help me understand how it also explains how the earth continues to rotate with very little angular deceleration?

Note:

This is not a duplicate of

  1. Why does the Earth rotate?

  2. What keeps the earth spinning?

because my question is specifically about why inertia is a reason for it to keep spinning.

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  • $\begingroup$ Inertia only means things go in a straight line if there are no forces acting on them. Bring in gravity and things still have inertia, but they don't travel in straight lines. $\endgroup$ – Mike Dunlavey Feb 20 '17 at 14:08
  • $\begingroup$ Related: physics.stackexchange.com/q/12140/2451 and links therein. $\endgroup$ – Qmechanic Feb 20 '17 at 14:24
  • $\begingroup$ "It continues to spin because of inertia." is wrong. it is the moment of inertia, not inertia, for rotations en.wikipedia.org/wiki/Moment_of_inertia $\endgroup$ – anna v Feb 20 '17 at 16:01
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Actually concept of inertia and conservation of momentum are similar. Conservation of angular momentum states that in absence of an external torque, body continues to rotate with the constant angular velocity. This tendency of any object to continue rotation with constant angular velocity is termed as Moment of Inertia (inertia in case of linear motion). It is function of distribution of mass of the body.

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The two explanations are closely related. There is inertia in a rotational motion and this is contained in the so called inertia tensor or in simpler terms the moment of inertia. This object, which actually depends on mass, plays in rotational dynamics, the same role mass plays in straight line motion. It gives a resistance to an angular acceleration. The higher the moment of inertia of a body, the more difficult is to impose angular acceleration.

Even though the conservation of angular momentum is a good and practical way of explaining the (nearly) conservation of the Earth's spin, the deep physical intuition is in the concept of inertia. In the limit that the moment of inertia goes to zero, the torque needed to accelerate (or decelerate) the body tends towards zero. It means that if there were no inertia (more precisely, when it tends towards zero) the spin of the Earth could increase or decrease arbitrarily fast even for external torque approaching zero. This can be seen from the Newton's second law for a rigid body rotating along a fixed axis, $$\tau=I\alpha,$$ where $\tau$ is the external torque, $\alpha$ is the angular acceleration and $I$ is the moment of inertia. When $I\rightarrow 0$ and $\tau\rightarrow0$, then $\alpha$ is arbitrary. Note that the angular momentum would still be conserved, since its rate is $$\frac{dL}{dt}=I\alpha.$$ However the angular momentum itself (as well as linear momentum) would be meaningless without inertia since it depends on mass. It is the existence of inertial mass that makes the dynamical quantities $L$ and $p=mv$ the relevant ones. Therefore, although the explanations are closely related, the meaning of inertia is more fundamental than the meaning of angular momentum or its conservation.

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  • $\begingroup$ 1st paragraph good, 2nd paragraph unnecessary and confusing IMO. $\endgroup$ – sammy gerbil Feb 20 '17 at 18:45
  • $\begingroup$ @sammygerbil Would you please give it another look? I rewrote the last paragraph. $\endgroup$ – Diracology Feb 20 '17 at 19:37
  • $\begingroup$ That is an improvement in clarity, but it seems to me that it does not add much to the argument. But that is only my opinion. $\endgroup$ – sammy gerbil Feb 21 '17 at 1:41
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I assume that you are happy with the idea that, when a spaceprobe is launched towards Mars, once it's rocket engine gives it enough velocity, it can be turned off, as there is nothing in the vacuum of space that slows the rocket down. The probe is provided with inertia, which requires a force to change it.

You can apply the same reasoning to the rotation of the Earth. After it formed from the accrection of material and given it's initial velocity, it would in theory continue to rotate with the same velocity because of conservation of angular momentum. The Earth was given an inertia, around its axis, which requires a force to alter it.

In practice, there are forces acting to change the inertia of the Earth. We have to take into account the effect of the moon, which through the action of the tides (as well as on the solid material) of the Earth, is gradually slowing the Earth down.

From Initial Velocity of the Earth

Scientists think that a large object, perhaps the size of Mars, impacted our young planet, knocking out a chunk of material that eventually became our Moon. This collision set Earth spinning at a faster rate. Scientists estimate that a day in the life of early Earth was only about 6 hours long.

The Moon formed much closer to Earth than it is today. As Earth rotates, the Moon's gravity causes the oceans to seem to rise and fall. (The Sun also does this, but not as much.) There is a little bit of friction between the tides and the turning Earth, causing the rotation to slow down just a little. As Earth slows, it lets the Moon creep away.

You also need to note that the inner core of the Earth rotates faster than the surface, Inner Core

The inner core rotates in the same direction as the Earth and slightly faster, completing its once-a-day rotation about two-thirds of a second faster than the entire Earth. Over the past 100 years that extra speed has gained the core a quarter-turn on the planet as a whole, the scientists found. Such motion is remarkably fast for geological movements -- some 100,000 times faster than the drift of continents, they noted. The scientists made their finding by measuring changes in the speed of earthquake-generated seismic waves that pass through the inner core.

This inner material has a different inertial value than the slower inertial value of the outer regions and surface of the planet.

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protected by Qmechanic Feb 20 '17 at 16:04

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