rotation vs revolution?
138870
rotation - spin around itself (center of axis)\n\nrevolution - spin around something else (which forms center).
256767
I'm not sure I really understand your question.  Are you how fast a particular point on earth is moving?  If that is the case it's not an easy answer because it depends where you are on the planet.  If you are on one of the poles then there is very little rotational speed.  If you are on the equator then your velocity is much greater.  Think of it like a CD in a CD player.  Also you would need to factor in the speed of the earth as it travels around the sun sometimes spinning in the same direction the earth is traveling resulting in a greater total velocity and sometimes spinning in the opposite direction yielding a lower total velocity.  The final analogy would be to tie a CD player to a string and swing it in circles while the CD is playing.  The speed of a single point, other than the center, of the CD is constantly changing.  However, it's still not even that simple due to the earth's eliptical orbit and varied velocity.
452210
Egads.  It's been quite awhile.  I remember some papers at SIGGRAPH a decade or so ago on this topic.\n\nAlright, here's a stab at the explanation.\n\nWith Euler mechanics or Euler angles, there are three reference angles: yaw, pitch, and roll. It is possible to rotate an object using these three reference angles such that two line up causing the inability to do an arbitrary rotation.  Say you roll to the right 90 degrees and this lines up the yaw axis with your pitch axis -- gimble lock results.\n\nWith quaternions, you don't have three reference angles.  You have only one plane and an arbitrary axis of rotation.  Each move creates a new plane and axis of rotation.  As such, there are no additional axes of rotation with which to collide because there is only one axis of rotation and it's position is arbitrary where as with Euler angles, the reference angles are fixed.\n\nI don't know if I've done it justice, but maybe this explanation and the references below will help you stitch together an understanding.
552911
The general rotation transform function is to multiply its coordinate in complex coordination by the transform function of R(teta)=cos(teta)+i*sin(teta) where teta is the transform (rotation) angle and i is the imaginary unique value.\nSuppose coordination of your point is (x,y); so the transformed point (x',y') would be:\nx'+i*y'=(x+i*y)*\n        [cos(teta)+i*sin(teta)]\n       =[x*cos(teta)-y*sin(teta)]+\n        i*[x*sin(teta)+y*cos(teta)]\ntherefore:\nx'=x*cos(teta)-y*sin(teta)\ny'=x*sin(teta)+y*cos(teta)\n\nin your example, the point (-5,10) after rotation of 30 degrees counterclockwise will be transformed to:\nx'=-5*cos(30)-10*sin(30)~ -9.33\ny'=-5*sin(30)+10*cos(30)~ +6.16
356220
Depends on your point of view. If you're hovering above the North pole, the earth rotates counter-clockwise. If you're hovering above the South pole, it rotates clockwise.
596684
The correct option is 'rotation of the earth'. When earth revolves, some part of it is directly facing the sun, and the other part is not. That explains the presence of day in one part of the world, and night in the other.
600116
Lets see now, Earth rotates aproximately once every 24 hours, thats one over 60 x 60 X 24, thats one over 86400 rotations per second. All the time we are doing that, consider this, we are also going around the sun at aproximately 66500 miles per hour.
745809
1 revolution  =2*3.1416 (pi) radian.\n\nSo, a revolution = pi radias i.e; 3.1416 radian
100448
There are 2 x pi radians per revolution, by definition of radian.  So \n\n45 rev./min x 1 min/(60 s) x 2 PI rad/rev =4.71 rad/s
831067
Any kind of spinning top is a gyroscope.  So building one is straight forward.  Not really sure what you mean about "displacement"?  Gyroscopes are to stop displacement but their size depends are what you can steady with the rotation of the gyroscope.
1134535
Moon definitely rotates on its axis and the period of its rotation is exactly equal to period of its revolution. So we always see the same face. \nIf earth was to rotate on its axis in 365 days. i.e. its period of rotation would had been equal to its period of revolution.it would always keep the same face to sun and there would be no days and nights. \n ==>>Note that the fact moon keeps same face towards earth is sufficient proof that it is rotating. otherwise if it revolves around earth, we would be seing the back of moon at some  time.
594072
frontside 180 360 flip\nhalf cab 360 flip
399435
transformed shape X for example.\n\nWhen writing transformations out. You should always say (in this case for a rotation)\n\nShape X is rotated 90 degrees clockwise about point (1,1) onto transformed Shape Y.\n\nThis may not be correct, but that's what we were taught in school... and lets just say A*'s are my worst marks :)
217587
First I want to clear up that clockwise is really a 2-dimensional description of rotation, and planet rotation can be viewed in 3D so you can't really describe planet rotation as clockwise or counterclockwise. If you define an "up" and a "down" for the solar system, and then say "when viewed from above the solar system rotates counterclockwise", then the "anticlockwise" description works. For my answer we will assume you have done all this and that the solar system rotates counterclockwise, so there is no confusion from the wording of the question.\n\nThe reason the solar system rotates counterclockwise has to do with the way the gas clouds that created the solar system collided. They didn't collide head on. Think of cars travelling in opposite direction down an interstate hitting each other not quite head on (i.e. the left headlights of both cars smack together). When they do this they will spin out sideways - they will effectively rotate around each other (in North America with the cars driving on the right side of the road, they will rotate counterclockwise when viewed from above if they collide like this). The gas clouds did the same thing and their collision exceeded the critical density needed for gravity to take over and start forming the solar system, and as this matter collapsed to form the sun and planets, the rotation sped up. The rotation these gas clouds got from their collision gave momentum to the rotation of most matter in the solar system; the sun rotates in the same direction as those clouds did when they collided and so does most other things, including all the planets.\n\nSo that is why.
199932
The earth's rotation.
894851
If you mean revolutions or rotations around its axis as defined by the frame of reference provided by the Sun, it's about 365 and 1/4 per solar year.
800991
180 degrees is equivalent to pi radians. Think about a circle (even better the unit circle). \n\nOne whole revolution is 360 degrees, or 2 pi, so 180 degrees is half of 360, thus it's pi. \n\nThe coordinates of pi on the Unit Circle is (-1, 0), if you wanted to know.