# Angular speed of two points on a circle.

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A disk is rotating CCW with an angular speed omega.

Two stickers A and B are fixed to different locations on the disk as shown.

Compare the angular speed of the two stickers A and B.

This problem is from one of the lecture slides. Can someone give me a good explanation of why the angular speeds of A and B are the same, but why the linear speed of B is greater than A?

The angular speed describes how much rotational angle (usually in radians) are cover per unit time. Being on the same rotational object, if one point goes around certain angle, e.g., $2\pi$ for a complete circle, any other points on the same object would also experience an rotation of $2\pi$. Therefore the angular displacement/velocity/acceleration for any points on the same rotational object would be the same.

The linear speed depends on the distance between the point of interest and the rotational axis. And you will have $v=\omega R$, where R is the distance between the point of interest and the rotational axis.
answered Oct 28, 2013 by (21,750 points)