Answer:
[tex]v=wr[/tex]
Explanation:
Tangent and Angular Velocities
In the uniform circular motion, an object describes the same angles in the same times. If [tex]\theta[/tex] is the angle formed by the trajectory of the object in a time t, then its angular velocity is
[tex]\displaystyle w=\frac{\theta}{t}[/tex]
if [tex]\theta[/tex] is expressed in radians and t in seconds the units of w is rad/s. If the circular motion is uniform, the object forms an angle [tex]2\theta[/tex] in 2t, or [tex]3\theta[/tex] in 3t, etc. Thus the angular velocity is constant.
The magnitude of the tangent or linear velocity is computed as the ratio between the arc length and the time taken to travel that distance:
[tex]\displaystyle v=\frac{\theta r}{t}[/tex]
Replacing the formula for w, we have
[tex]\boxed{ v=wr}[/tex]
