In rotational motion, the linear velocity ( ) of a point on a rotating object is related to the period ( ) of rotation through the relationship between linear velocity, angular velocity, and the radius of the circular path.
where is the period, or the time it takes for one complete rotation.
where is the radius of the circular path, and is the angular velocity.
To express linear velocity in terms of the period , substitute the expression for from the first equation into the second equation:
Simplifying gives:
This equation shows that the linear velocity is directly proportional to the radius and inversely proportional to the period .
In essence, the faster the object rotates (shorter period), or the larger the radius, the greater the linear velocity of a point on the object.
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