Apparatus Competition

2006 AAPT Summer Meeting

Syracuse, NY


Moments of Inertia

What’s inside a baseball?


Harriet Slogoff and Bob Smith

University of Pennsylvania

209 South 33rd Street

Philadelphia, PA  19104-6396



slogoff ‘at’ physics ‘dot’ upenn ‘dot’ edu


Is there any way (short of cutting it open) to learn how the mass of a ball is actually distributed inside the spherical exterior surface? Here is one way, developed by Prof. Howard Brody to analyze tennis balls for the International Tennis Federation. [1]


The moment of inertia (I) is measured about an axis through the center of mass using a torsion pendulum. Using an object of known moment of inertia such as a uniform disk on the end of the torsion wire and measuring T0, the period of the oscillation, the torsion constant k for the pendulum can be determined:


            The moment of inertia of any object (Ib) can be determined by attaching the object to the disk on the end of the pendulum and measuring the new period of the oscillation. The total moment of inertia will be:


The new period of oscillation is Tt , and the total moment of inertia is  .   Substituting Eq. (1) and this equation in Eq. (2) gives the unknown moment of inertia:


A metal disk of mass 0.0595 kg (including the attached disk magnet) and diameter of 0.101 m is attached to the end of the torsion wire using a wire gauge drill chuck (micro chuck).  A 5-40 nut was soldered to the disk, and a small hole was drilled in the center of the disk, slightly larger than the threaded hole in the nut to allow the micro chuck to be screwed to the disk. The threaded shaft of the micro chuck must be cut down so the magnet will lie flat. The neodymium disk magnet is placed underneath the disk at the center to allow for attaching the ball.  Each ball must have a steel self tapping screw (for soft materials) or a steel machine screw (for hard material) attached so that it can be suspended from the disk and magnet.


The wire we used is piano wire with a diameter of 0.30mm.  The other end of the wire is attached to a second micro chuck which is screwed into a stainless steel rod. The entire apparatus is shown below.


Parts List:


















Text Box: Figure 1: The metal disk, micro chuck, Neodymium magnet and a golf ball




Text Box: Figure 2: The complete apparatus with rods and clamps

[1] H.Brody, "The Moment of Inertia of a Tennis Ball,"Phys.Teach. 43, 503-505 (2005)