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mechanics angular velocity (1 Viewer)

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InteGrand

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swagswagyoloswag said:
https://9eeba4054ee764a743f35bb25b5.../4U/James Ruse 2014 4U Trials & Solutions.pdf

q16 a i)
why is the angular velocity about B = -pi/2 ?
It makes sense, because it closes as P moves around, but I thought angular velocity is always in respect to the POSITIVE x-axis? angle PBC = 90+ theta/2, hence angular velocity = + pi/2?
Click to expand...
http://community.boredofstudies.org...on-2/337525/2014-james-ruse-question-16a.html

(porcupinetree's solution to that Q is in one of his images there)
 
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swagswagyoloswag said:
I get that, but why did he/solutions find angle PBA? I thought angular velocity is respect to positive x-axis (direction of angles) so I should find angle PBC?
Click to expand...
That's because it's asking for the angular velocity about A and about B. The angular velocity about A refers to how P's angle with respect to A (namely angle PAB) changes, and similarly for B, it is angle PBA. This is because the relevant angle is the angle between the segment joining P to the point in question, and the diameter of the circle (because P is moving on this circle; if P were moving on some other circle, it'd be that circle's diameter instead).

The positive x-axis thing essentially refers to how much (angle) P has rotated compared to its starting position.
 
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