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(The following answer was written to address the original version of this question, which was simply "Does General Relativity theory correctly explain the ellipsoidal shape of the earth?") Yes. General relativity predicts that the equator will bulge out just enough such that the reduction in gravitational time dilatation at the equator relative to the ...


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Comment to the question (v1): Besides what John Rennie wrote in his correct answer, note that the velocity profile of an irrotational/free vortex falls off as $$\tag{1} v~\propto~ 1/r,$$ while a galactic rotation curve may actually increase with $r$, and in any case, it never falls off faster than$^1$ $$\tag{2} v~\propto ~1/\sqrt{r},$$ so the analogy ...


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General remarks. That's right. Torque is defined as $\mathbf r\times\mathbf F$ where $\mathbf r$ is the position where the force is applied, and $\mathbf F$ is the force being applied. The so-called Law of the Lever can then be derived from the following fact (which itself can be derived from Newton's Laws) about systems of particles: The net external ...


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If we take the Milky Way as an example, the black hole at the centre, Sagittarius A$^*$, has a mass of about 4 million times the Sun. However the mass of the Milky Way is somewhere around a trillion Suns. So the central black hole makes up 0.0004% of the total mass. While the central black hole may have been important in the formation of the Milky Way, its ...


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The "missing" kinetic energy is still there ... it's now in the rotation of the yo-yo.


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As others have already pointed out, the moment of inertia depends mostly on the mass distribution. As an example, imagine two cylinders with exactly the same mass. Suppose that you cannot see what is inside them, it's covered on both ends (and the covers mass is negligible). The first is a solid cylinder. The second one is a hollow cylinder. Ka-boom! ...


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Why would there be no radius in torque? A real torque is a real force that acts on a real rotating body (rigid or not) at a real radius. If you look at e.g. rotating machine parts, they all have a finite diameter. That diameter is of enormous importance for the design of a part, because together with the material constants it determines just how much torque ...


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The physical explanation for why torque increases with r is that the longer the lever arm is the greater angular acceleration you can cause for a given force F. If a screw is stuck because it was screwed in too hard (ie with too much torque), you need to get a longer wrench. With the longer wrench (ie, larger r_w) you can generate greater force at the edge ...


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It's part and parcel of the definitions of angular momentum and torque. Consider a system of particles, not necessarily a rigid body. Without loss of generality, we can use an inertial frame that is instantaneously co-located and co-moving with the system center of mass. The angular momentum of the system with respect to the origin of this frame is defined ...


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If the object is not spinning, then moving it will take the same effort whether the mass is spread out, or all at one point. Imagine that you are on a roundabout, but you are sitting on a disk that it itself able to spin. Initially you are facing North, and you are exactly in the middle of your disk (although it is off axis of the roundabout). Now the ...


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This is a very late response, but there is no accepted answer as of yet, and none of the answer quite hit the mark. Regarding the magical collision hypothesis, that smacks of being rather non-scientific. Scientists as well as Missourians are wont to say, "Show me!" Other than the fact that Venus's rotation is anomalous, what, exactly, is the evidence for ...


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Can a ball stay still while laying on a inclined plane? In freshmen physics, the inclined plane and ball are perfect and the ball moves, so for your purposes, no. If either the surface or the ball have imperfections, we can tip the plane and the ball won't move until gravity exceeds the sum of the normal forces. To imagine those normal forces, we look ...


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The problem with attempting to do the analysis with the forward point of contact on the box when it is sliding is that the box is accelerating. This makes a non-inertial frame and there's more moving parts. Besides the force of gravity on the center of mass, there will be fictitious forces. First, lets assume friction is zero. If so, we can calculate ...


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A few clarifications first: I will assume that the bigger cylinder (radius $R$) is not moving, and I will be doing the problem in this frames. I will assume that both $\theta$ and $\phi$ are positive in the clockwise direction. This is against convention but it'll make a few negative signs disappear, and you many find it easier to think this way given how ...


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If motor A does the same job as motor B, but with a 10x greater load, and the mechanical advantage (gearing etc) is the same, then I would expect that the torque that A supplies is ten times greater as well. But that is not quite how you phrased the question. It necessarily follows that a higher HP motor can supply greater torque - at least, with the right ...


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It makes the problem easier to visualize if you collapse to 2 dimensions and imagine a circle in the same situation with homogeneous distribution of mass effectively centered at the center of the circle. Constrained initially by contact with the table's edge, and after your nearly forceless nudge the center will begin to accelerate through an angle under its ...


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If you impact the second body its axis of percussion it will purely rotate. By carefully choosing the inertial properties of the two objects you can make the first object stop translating in the process. See this post for more details on a particle to rod impact.


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Yes, the shape of the Earth is consistent with general relativity. Thirring's equations are not an indication that general relativity predicts results that are inconsistent with the observed shape of the Earth, in large part because Thirring's equations applied general relativity incorrectly. For clarity, this question and answer are purely about ...



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