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11

Not sure if I can add much to Kyle's comment, but I'll try. Looking closely, he starts with no angular momentum about the vertical axis - the take-off is "straight". Then he moves one arm behind himself and then extends it sideways - generating a torque about the vertical axis. By tucking his other arm in tightly, his body can now rotate. At the end of the ...


10

One of my favorite scientific papers of all times (mainly because it's rather bizarre) explains the basics of what's going on here. That paper is Kane & Scher, "A dynamical explanation of the falling cat phenomenon," International Journal of Solids and Structures 5.7 (1969): 663-666. To get even more mathematical, there's Montgomery, "Gauge theory of the ...


5

(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 ...


5

The Earth's rotation rate and the location of the rotation axis change over time. These collectively are called the Earth orientation parameters. On very short time scales, a day or less, the changes in the Earth orientation parameters result predominantly because of the ocean tides. On the scale of decades to a century or so, the dominant driver is exchange ...


4

There are two and possibly three factors at work here: Factor 1: Nonscalar Inertia Matrix: Angular Momentum and Velocity have Generally Different Directions One which I don't think has been mentioned is that unless a body is rotating about a so-called principal axis, in general the angular momentum and the angular velocity vectors do not point in the same ...


2

Made visualisations so you can see how it looks like. Rotating X: Rotating X and Y: Rotating X,Y and Z:


2

1.) Angular momentum is always with respect to a reference point. A massive particle moving on a straight line with momentum $\vec{p}$ will have angular momentum with respect to any point that is not on the worldline of the particle (since $\vec{r}$ and $\vec{p}$ will not be parallel, i.e. $\vec{r}\times\vec{p}\not=0$). Therefore, bodys can posses angular ...


2

The dominant hypothesis regarding the formation of the Moon is that a Mars-sized object collided with the proto-Earth 4.5 billion years ago. The Earth is rotating now because of that collision 4.5 billion years ago. As the linked question shows, angular momentum is a conserved quantity. Just as something has to happen to make a moving object change its ...


1

Yes, but only very slightly as the Earth is much heavier than the atmosphere. If you were accelerating at the equator you would exchange angular momentum with Earth, slowing or accelerating it's rotation, depending which way you accelerate. Same goes for air masses, as they accelerate when they warm up or cool down and move more one way as the other way is ...


1

The answer is that at any moment a rigid body is rotating about an arbitrary axis, with an arbitrary angle. There are two components defining the direction of rotation axis, and one for the magnitude of rotation. Often we transform these three quantities into three sequential rotations called Euler Angles. If you look up rotation matrix you will find all ...


1

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 ...


1

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 ...


1

If your fan is not connected to anything, and the blades do not encounter any air drag (outer space) then conservation of momentum means that the blades will turn in one direction, and the motor assembly in the other direction If you know the moment of inertia of the blades, call it $I_b$, and of the motor, $I_m$, then the ratio of the angular velocity ...


1

If, neglecting friction, I keep both top and bottom of the fan free to move (like maybe in outer space), and I turn on the fan, what will happen? Some satellites use something very much like this to keep the satellite pointing in the right direction, and do so without using rockets. It's called a reaction wheel. The motor is rigidly connected to the ...


1

I am confused regarding the fact that when a disk is rolling on an inclined plane without slipping and similarly a solid sphere is rolling on an inclined plane without slipping then the sphere has more angular velocity. the moment of inertia of a sphere is less than the disk so it that if the moment of inertia is less then the angular velocity is more? ...


1

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 ...


1

I suppose you could try to think of the problem in another way. What would happen to a cylinder (or sphere) if you put it on a frictionless inclined plane? Would it still roll or just slide? The imbalance in forces acting on the cylinder at different points, with respect to its center of mass, are what lead to the rotation. Gravity acts on the center of ...


1

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 ...


1

I would try to explain very briefly. When you apply a force onto a body, it causes the body to move in the line of application of force. This introduces translational motion into the body. When you apply a torque onto a body, it causes the body to rotate about a point. This introduces rotational motion into the body. Torque in rotation is analogous to ...


1

Force represents an energy transfered (and applied in general in a straight line). On the other hand Torque represents a force acting on a point on a straight line but the effects are applied elsewhere (in rotating the body). As such there is (at least) this subtle difference. The force is applied to a point of the body which then (by internal constraints ...


1

There is not a simple answer for this since it is both yes and no. From an internal frame of reference: Looking at the object, nothing is happening. Looking at the outside world, it is moving in a predictable pattern. From an external frame of reference: The rotation on one axis is easy to see. The rotation on 2 axes looks like a rotation on a moving axis. ...



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