Q6.2 Visualising angular velocities (S)

A plate is suspended horizontally in mid-air. The center of the plate defines the origin of a coordinate system with the z axis vertical.

Draw diagrams to describe the motion of the plate if it has angular velocity:

  1. $\vec{\omega} = c\hat{k}\,\,rad\, s^{-1}$ about the origin.
  2. $\vec{\omega} = -c\hat{j}\,\,rad\, s^{-1}$ about the origin.
  3. $\vec{\omega} = c\hat{k}\,\,rad\, s^{-1}$ about the point $\hat{i}+\hat{j}$.

where c is a positive constant and $\hat{i},\hat{j},\hat{k}$ are unit vectors along x,y,z.

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Hint

Draw some nice diagrams, and remember what axis to rotate about.
 

Solution

Reveal
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Solution

  1. Plate rotates anti-clockwise about an axis through its centre and into the plane (clockwise about the z-axis, which points out of the plane).
  2. Plate rotates anticlockwise about y axis
  3. Plate rotates anti-clockwise about an axis through the point (1,1), and into the plane.
Graphic - No title - plates