Rotation of line about rotating axis

In summary, the conversation discusses the properties of axis A and B, the line MN, and the rotations in the plane of the circle. It is mentioned that axis A is always normal to the plane of the circle and passes through the centre of the circle, while axis B is always parallel to the plane of the circle and the y-axis of the lab frame, and also passes through the centre of the circle. The line MN is described as an infinitely long line that lies on the plane of the circle and rotates about axis A with an angular velocity of w1. The plane of the circle itself also rotates about axis B with an angular velocity of w2. It is stated that if the angular velocities are not equal and do not have a
  • #1
hackhard
183
15
axis A is always normal to plane of the circle and passes thru centre of circle
axis B is always parallel to plane of circle and is always parallel to y- axis of lab frame.
axis B passes thru centre of the circle
the infinitely long line MN always lies on the plane of the circle and passes thru centre of circle
the line MN rotates (in plane of circle) about axis A. with angular velo "w1"
the plane of circle itself rotates about axis B with angular velo "w2"
if w1 is not equal to w2 and
w1 is not equal to w2 / 2 and
w1 /2 is not equal to w2
then -
will the line MN (at some point of time) pass thru every point (coordinates defined wrt lab frame) in 3d space?
(rotations continue forever)

DSC05749.JPG
 
Last edited:
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  • #2
If ##i * \omega_1 = j * \omega_2## (with i, j integers) then it's easy to see that MN sweeps through the xy plane at fixed positions. So it's a matter of common dividers. You only excluded i = 2, j = 1.
 
  • #3
BvU said:
If ##i * \omega_1 = j * \omega_2## (with i, j integers) then it's easy to see that MN sweeps through the xy plane at fixed positions. So it's a matter of common dividers. You only excluded i = 2, j = 1.
i am adding 3 points to my initial question-
w1 is not an integral multiple of w2
w2 is not an integral multiple of w1
axis B is fixed wrt lab frame

my question remains unchanged -
hackhard said:
will the line MN (at some point of time) pass thru every point (coordinates defined wrt lab frame) in 3d space?
 
  • #4
Moving the goalposts while playing, eh ? Do you know about Lissajous figures ? Your casus is analogous in every possible respect if you think of spherical angular coordinates ##\theta## and ##\phi## instead of x and y.
 

What is rotation of a line about a rotating axis?

Rotation of a line about a rotating axis is the process of rotating a line around a fixed point or axis. This results in the line changing its orientation and position in space.

What is the difference between rotation and translation?

Rotation involves moving an object around a fixed point or axis, while translation involves moving an object from one location to another without changing its orientation.

What is the formula for calculating rotation of a line about a rotating axis?

The formula for calculating rotation is: x' = x*cosθ - y*sinθ y' = x*sinθ + y*cosθ where (x,y) are the original coordinates and (x',y') are the new coordinates after rotation by an angle θ.

What factors affect the amount of rotation of a line?

The amount of rotation of a line is affected by the angle of rotation, the distance from the rotating axis, and the direction of rotation (clockwise or counterclockwise).

How is rotation of a line used in real-world applications?

Rotation of a line is used in various fields such as engineering, architecture, and computer graphics. It is used to design and create objects with specific angles and orientations, as well as to animate objects in computer graphics and simulations.

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