Calculate Rotational Velocity of Object Around Fixed Point

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SUMMARY

The discussion focuses on calculating the rotational velocity of an object around a fixed point, specifically using the example of a clock hand. It is established that the rotational velocity (v) increases proportionally with the radius (r), defined by the formula [nu] = v/r, where [nu] represents angular velocity in radians per second. The relationship between arc length (a) and angular displacement ([alpha]) is also clarified, with [alpha] = a/r. This means that while the velocity varies along the length of the hand, the angular velocity remains constant across all points.

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einsteinian77
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How could i calculate the velocity of an object rotated around a fixed point such as a hand on a clock. It seems as though each section of the hand would have a different velocity, the end part being the fastest while the beginning part being the slowest if not moving at all. I am guessing the velocity would be expressed in frequency somehow.
 
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Originally posted by einsteinian77
Im guessing the velocity would be expressed in frequency somehow.

That's correct, einsteinian77. Since the rotational velocity v increases proportional with radius r (distance from center), you define the angular velocity
[nu] = v/r.
This is the same for all points. The unit is 1/s. You could also say it's radians per second, since by integrating you get the angle:
[alpha] = a/r
where a is the arc length, and [alpha] is measured in radians.
 
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