From: Ronald Wong (ronwong@inreach.com)
Date: Mon Dec 20 1999 - 10:20:13 PST
Date: Mon, 20 Dec 1999 10:20:13 -0800 (PST) Message-Id: <l03102801b48322273e30@[209.209.18.52]> From: Ronald Wong <ronwong@inreach.com> Subject: Re: Angular displacement
Marc Afifi asked:
>
> Could someone explain how it is possible to have an
> angular displacement greater than 2pi radians? Does
> the word displacement have a different meaning in
> rotational kinematics than it does in linear
> kinematics? Is there a corresponding term for distance
> in rotational kinematics?
>
Good questions Marc. If all you are dealing with is the rotational motion
of an object about a given axis, there definitely wouldn't seem to be any
point in talking about angular displacements greater than 2pi radians. The
object will return to an earlier position once it has rotated through 2pi
radians or more.
Sometimes rotational motions are connected to linear motions. It is here
that angular displacements greater than 2pi prove to be of some consequence.
A couple of simple examples of this would be a wheel rolling along a
surface without slipping as it moves along or a weight hanging from a cord
that passes - without slipping - over a pulley.
In the first case, the linear distance traveled by the center of the wheel
is the wheel's radius times the angular displacement in radians. In the
second case, the linear distance that the hanging weight moves (up or down)
is the radius of the pulley times it's angular displacement in radians.
In these examples, it is important to take into account the fact that the
angular displacement can be greater than 2pi. After one, two, or three
revolutions the wheel or pulley will be right in the same positions that
they started with but the wheel or weight will have moved linearly through
3 different places in that time.
So much for kinematics. - ron
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