# Not Really Pendulum mechanics

James Rogers (jamesr@best.com)
Fri, 18 Jul 1997 23:22:23 -0700

At 10:26 PM 7/18/97 -0400, you wrote:
>Damien Broderick wrote:
>>
>> At 08:13 PM 7/17/97 -0400, Mike Lorrey of spacedrive fame wrote:
>>
>> >How can a little kid (or an adult for that matter) sit on a perfectly
>> >still playground swing, begin rocking back and forth, and within a
>> >minute be wizzing back and forth to a pretty good height, without ever
>> >touching the ground or other still grounded object?
>>
>> Michael, Michael! It's connected at the top. (Unlike the spaceship.)
>>
>
>That doesn't mean anything. As a pivot point it is merely a fulcrum if
>reaction mass is expended, according to Newton's Third Law. Since the
>rider on the swing is at a standstill, and has no way to push against
>anything, how do they develop the significant levels of momentum they
>do?

The pivot point acts as the connection point between a fixed and multiple
free-moving members, not really a pendulum in the classical analysis sense.

If it were a simple pendulum problem, it would not be possible for a person
to start from rest.

The force that you have forgotten is the tension in the rope. Analysis as
a classical pendulum generally excludes this force because 1) it is in
equilibrium, and 2) it is contained in a single member. When the swinger
pulls on the rope at some point between the seat and the pivot, the x-axis
component of the tension is modified, evidenced by the sudden bend in the
rope around the point where the hands are attached (at which point the rope
should be analyzed as *two* individual free-moving members around an
additional pivot point). Because one point is fixed (the pivot) and the
other point is not (the seat), there is a net change in force around the
second pivot point (the hands). In other words, the swinger is actually
pulling themselves towards the pivot point, and the unbalanced x-axis
component of this applied force is manifested as acceleration. This is why
where you hold the rope makes a difference in how fast you gain speed.

This problem is really a classical multi-member statics (or dynamics
depending on your analysis technique) problem.

-James Rogers
jamesr@best.com