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I maybe seriously underestimating the OP's question (and not quite sure if I understand it) but I believe he/she is simply asking why we only need two quantities (rotation and translation) to describe 3D space. I'll start with 2 dimensions: Imagine you're playing the game Asteroids and you want to move your spaceship a little to the right to get out of the ...


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"Rest, in physics, refers to an object being stationary relative to a particular frame of reference or another object." - Wikipedia (emphasis mine) While on Earth, the planet is often treated as the default frame of reference. It is not a perfect frame of reference, but for many purposes it is good enough. Since there is no absolute frame of reference, ...


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No matter how many spacial dimensions, there is only one kind of line. Two points describe a line and between them is only one dimension. For rotation, again it doesn't matter which way it's rotating, but the number od possibilities increases with dimensions. The question is whether any combination of rotating (instantaneous) can be combined to a single ...


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"A state of rest" is a relative term. Relative means - measured in comparison to the things around it. When you sit in a train and sip from a cup of coffee, you can do so because the cup is still relative to you even though both of you might be hurtling through the countryside at 200 km/h. For most experiments, objects can be considered "at rest" if they ...


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Revolving around the sun is equivalent to free fall around the sun, so the revolution allows you not to 'feel' the sun's gravity. The rotation of the earth is something that can be measured: (i) a centrifugal force which is a small offset on gravity, and (ii) causes the coriolis force. Both these are small effects, so can often be ignored for laboratory ...


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When you're in a moving vehicle and see trees or buildings, who is moving? Are you moving forward, or are the trees and buildings moving backward? Its counter-intuitive for beginners but both these views are absolutely correct. We can only describe the motion of an object from a reference frame. A reference frame is a specific configuration from where you ...


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Solving lots of physics problems involved you choosing a frame of reference. As long as all your formulations are from a particular frame of reference, for example the energy of objects then the laws will work. Since you are also travelling with the object, (as the earth rotates) it is easier to say you are at rest. If you are travelling at constant velocity ...


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The three generators of right-handed spinor rotations are given by $\left\{- i\sigma_x,-i\sigma_y,-i\sigma_z\right\}$, see for instance Peskin & Schroeder page 44, and the rotation matrix for a spinor rotation over an angle $\phi$ around a unit vector $\hat{s}$ is given by: $R~=~ \exp\left(-i\frac{\phi}{2}~\hat{s}\cdot\vec{\sigma}\right) ~=~ ...


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Venus has an axial tilt of 177$^\circ$, so it rotates backwards compared to the majority of other planets. It also has an extremely slow rotation rate of one rotation every 244 days. In comparison, Uranus rotates every 17 hours, but has an axial tilt of 98$^\circ$. It rotates in a direction almost in the same plane as its orbital motion. It seems very ...


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In theory there is no torque from friction once the cylinder is rolling. Imagine that there is no supporting surface but no gravity - then the cylinder will just continue to "roll" forever. So all the supporting surface needs to provide to the cylinder is a force through its centre of mass to counteract the gravitational force. This is a force perpendicular ...


1

Does a body always rotate purely about its center of mass? Well, that depends. The first assumption you need is that the body is rigid. Violate this assumption and all bets are off the table because you can't even necessarily classify all motions as "rotations": for example if a long thin board starts twisting sinusoidally into/out-of a helix shape, ...


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A body in free motion does not necessarily rotate about the center of mass. The center of mass might have straight linear motion in addition any rotation. The general motion is a screw motion with a rotation about some instantaneous axis and parallel translation at the same time. Consider an arbitrary body rotating by $\vec{\omega}$ and at some instant the ...


2

Any rigid body in motion can be described as rotating about in instantaneous axis of rotation (IAR) and translating along the same axis at the same time. Example/Proof A rigid body in moving and at time instant a point A riding on the rigid body has position vector $\vec{r}_A$ and instantaneous linear velocity $\vec{v}_A$ at A. The whole body is rotating ...


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No difficulties at all. If the net force applied on a body is zero then the center of mass is not going to move accelerate. This leads to the conclusion that the only motion allowed is a rotation about the center of mass. For more details refer to: http://physics.stackexchange.com/a/81078/392 The relevant equations are: $$ \mathbf{F} = m \,\mathbf{a}_C ...


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Given viscous effects, that is indeed the case if: We are looking at a steady state system It is not a rarefied gas (i.e. at pressures much lower than atmospheric) The walls of the container are rough enough such that the gas molecules don't 'slip' over the surface but can be assumed at the same angular velocity (i.e. the no-slip condition) Point 2 is ...



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