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Unformatted text preview: to form a line segment, the velocity of
the object on that line segment would be the same as the velocity on the circle. For this reason,
the quantity v is often called the linear velocity of the object in order to distinguish it from the
angular velocity, ω . Putting together the ideas of the previous paragraph, we get the following.
Equation 10.2. Velocity for Circular Motion: For an object moving on a circular path of
radius r with constant angular velocity ω , the (linear) velocity of the object is given by v = rω .
Mention must be made of units here. The units of v are length , the units of r are length only, and
the units of ω are radians . Thus the left hand side of the equation v = rω has units length , whereas
the right hand side has units length · radians = length·radians . The supposed contradiction in units is
resolved by remembering that radians are a dimensionless quantity and angles in radian measure
are identiﬁed with real numbers so that the units length·radians reduce to the units length . We are
long overdue for an exampl...
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