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Could someone please explain me why the velocity of point P and P' aren't the same? Appearently it is because the angular velocity of point A and B aren't the same.

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We are only given that the angular velocity of A is 10rad/s clockwise.

Why? I would think that, as these two elements are connected , they would all rotate with the same angular velocity. If A rotates with a speed of 10rad/s it would be logical for me that point B just follows and rotates with the same angular velocity.

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    $\begingroup$ Hint: angular velocity is defined with respect to an origin. What are $P$ and $A$ 's radiuses about that origin? $\endgroup$ Commented Dec 23, 2015 at 14:56
  • $\begingroup$ @CarlWitthoft: The distance PA is 159.3mm. So point P and P' have the same distance to point A. $\endgroup$ Commented Dec 23, 2015 at 15:05

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The velocity of P' is perpendicular to AD, and the velocity of P is perpendicular to BP. So clearly the directions are not the same. Thus there is relative velocity between P and P' as shown in the diagram. Now, if gyroscopes are mounted at D, P', or any point on AD, except A, they will all measure the same angular velocity. A gyroscope mounted at P will measure the same value as one mounted anywhere between B and P, excluding B.

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