ROTATIONAL DYNAMICS/MOMENT OF INERTIA
Unit 16 , Dr. John P. Cise, Professor of Physics, Austin Com. College, 1212 Rio Grande St., Austin Tx., 78701
[email protected] & New York Times , September 25, 2015 by Manohla Dargis
New York Film Festival Walks the Tightrope
(a) Find this performers
Between Art and Commerce QUESTIONS:
balancing rod’s mass in slugs? (b) Find this
rod’s moment of inertia (I) about the center in
units of slugs ft2? (c) Find the moment of
inertia (I) of this rod about it’s center in units
of Kg. m2 ?
HINTS: weight = m g , g = 32 ft./s.2 ,
IROD CENTER = (1/12) M L2, L = total
length of rod.
ANSWERS: (a) 0.97 slugs , (b) 122.95 slug ft.2
(c) 168 kg. m.2
Joseph Gordon-Levitt in Robert Zemeckis’s “The Walk,” opening the New York Film Festival.
This year’s New York Film Festival opens with a couple of virtuosic balancing acts. One, “The Walk,” the latest from
Robert Zemeckis, features Philippe Petit’s nosebleed stroll from one World Trade Center tower to its twin on Aug. 7,
1974. The other high-wire act is far less dangerous, but comes with its own hazards because it means pleasing
constituencies as different as film society patrons and everyday cinephiles, critics who complain that it’s too elitist and
those who sniff at the very idea of pleasurable, old-fashioned entertainment. It’s a tough trick, one the festival pulls off
by putting a crowd-pleaser like Mr. Zemeckis alongside the rarefied likes of Chantal Akerman.
INTRODUCTION: A wire-walker may use a pole for balance or may stretch out his arms perpendicular to his trunk in
the manner of a pole. This technique provides several advantages. It distributes mass away from the pivot point,
thereby increasing the moment of inertia. This reduces angular acceleration because a greater force is required
to rotate the performer over the wire. The result is less tipping. In addition the performer can also correct sway by
rotating the pole. This will create an equal and opposite torque on the body.The important insight is to think about it
as a rotational system, with the tightrope walker and his/her pole each rotating around the tightrope.
The horizontal pole has heavy weights on the end, serving two purposes: increasing the moment of
inertia of the pole and the amount of control over the net torque the tightrope walker has.An increased
moment of inertia helps withstand external sources of torque, such as sudden gusts of wind. The heavy weights
allow the tightrope walker to exert torque by simply rotating the pole slightly, which moves his/her center of mass the
other way, helping recenter him- or herself directly over the tightrope. One way to view the high-wire act is to see the
wire as an axis and the center of mass of the performer as having the potential to rotate about the axis. If the center
of mass is not directly above the wire, gravity will cause the performer to begin to rotate about the wire. If
this is not corrected, the performer will fall. The artist often carries a balancing pole that may be ((( as long
as 12 meters (39 feet) and weighs up to 14 kilograms (31 pounds)))). This pole increases the rotational inertia of
the artist, which allows more time to move his or her center of mass back to the desired position directly over the
wire. This effect can be magnified by making the pole as long as possible and by weighting its ends.The pole
also helps balance the funambulist by lowering the center of gravity. High-wire artists use drooping, rather than
rigid, balance poles. It's possible, in fact, to have such heavy weights attached to the ends of a long, drooping
pole that the center of gravity of the performer/pole system is below the wire. In this case, the performer
would require no more sense of balance than a person hanging from the wire.