Rotation of a rigid body about external axis

  • #1
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in the figure a rigid body - a circle- is moving such that its centre is moving in a circular path but the orientation of the body is fixed with respect to the centre of the body (the circle). According to def of rotion of rigid body -
Rotation of a rigid body about a fixed axis is defined as the motion in which all particles of the body move on circular paths with centers along the axis of rotation and planes of rotation normal to this axis.
Will the body (as a whole) be considered to be ROTATING about axis "A" ?
 

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  • #2
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Are the particles in the circle undergoing rotation about the centre of the circle? If yes, then the answer to your question is no.

If no, then yes the entire system can be said to be undergoing rotation about A.
 
  • #3
vanhees71
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The kinematics of the rigid body has 6 configuration degrees of freedom. They are defined by fixing an arbitrary reference frame in the body, e.g., by defining one point at rest relative to the body and a Cartesian coordinate system, also fixed at rest relative to the body. In addition you have an arbitrary inertial reference frame of the observer ("lab frame"). The complete position of the rigid body is then determined by three coordinates from the origin of the lab frame to the fixed point in the body (which you can conveniently choose as the center of mass) and the rotation of the body-fixed Cartesian basis system relative to the lab-frame Cartesian basis. The latter are usually chosen as three Euler angles.

In your case, the motion is such that the fixed point of the circle (I'd choose the center of the circle) is rotating around the point ##A##, fixed in the lab frame. Of course, also any body-fixed Cartesian system will necessarily undergo a rotation relative to the lab-fixed Cartesian system.
 
  • #4
A.T.
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the orientation of the body is fixed with respect to the centre of the body
An orientation cannot be fixed with respect to a point. It can be fixed fixed with respect to a set of axes.

all particles of the body move on circular paths with centers along the axis of rotation
And? Is that the case in the scenario you envision?
 
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  • #5
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I am making my question clear
in the figure a rigid body - a circle- is moving such that its centre is moving in a circular path but the orientation of the body is fixed with respect to the centre of the body (the circle). According to def of rotion of rigid body -
Rotation of a rigid body about a fixed axis is defined as the motion in which all particles of the body move on circular paths with centers along the axis of rotation and planes of rotation normal to this axis.

This a detailed diagram of the same scenario.
1st ) The centres of the circular paths of the all the particles of the body do not join to form a straight line which violates this -
all particles of the body move on circular paths with centers along the axis of rotation .

2nd) the line joining the centres of the circular paths of any 2 particles of the body is not normal to the plane of rotation,which violates this -
planes of rotation normal to this axis.
my question - Will the body (as a whole) be considered to be ROTATING about axis "B" ?
DSC05747.JPG
 
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  • #6
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All the particles in the rigid body are undergoing rotation about their own centre. The rigid body as a whole undergoes rotation about an axis outside the body. Both the angular velocities may or may not be different. The particles of the body are NOT undergoing rotation about the forementioned axis. Done.
 
  • #7
A.T.
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Will the body (as a whole) be considered to be ROTATING about axis "B" ?
No.

All the particles in the rigid body are undergoing rotation about their own centre.
They are undergoing translation along circular paths, not rotation.
 
  • #8
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They are undergoing translation along circular paths, not rotation.

I meant if they rotate they will do so about the circle's centre.
 
  • #9
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  • #10
vanhees71
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Sure, just fix a Cartesian system with the body with origin in B and rotate the entire body, including this body-fixed reference frame, around A. Then B will rotate around A but also the body-fixed reference frame will rotate.
 
  • #11
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Why should they?

Because I can choose to make them to. Its not a part of the original question "hackhard" asked. I was just stating it as a fact.
 

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