MadSci Network: Physics
Query:

Re: What is the effect of density or shape of a bowling balls inner core?

Date: Fri Mar 19 14:57:16 1999
Posted By: Tom Cull, Staff, Clinical Sciences MR Division, Picker International
Area of science: Physics
ID: 920876163.Ph
Message:

I did a bit of web research on bowling balls. I was amazed at the wonderfully descriptive language used for marketing bowling balls. I was not sure I was supposed be buying a ball or a car :)

A bowling ball starts out sliding on the lane oil and gradually begins to roll with little or no slipping. The amount of sliding a ball does is dependent on lane conditions and the surface of the bowling ball. Controlling the slide to roll condition is what separates the good bowler from the rest of us. A uniform density bowling ball has some distinct disadvantages to a ball with a core. A core is used to give a bowling ball the desired weight but closer to the center of the ball. An asymetric core can give the ball a preferred axis of rotation to minimize the effects unwanted side sliding during the sliding portion of the balls travel.

The core of a bowling ball is designed to put a significant percentage of the balls weight near the center of the ball. In this manner, the surface and outer layer of the bowling ball can be made of a light and durable material. The core can be made heavier or lighter to suit the desires of the bowler (or the sales pitch of the manufacturer). Typically bowling balls fall in the weight range of 12 to 16 pounds. The kinetic energy of a rolling object is given by:

KE = 1/2 * M * V2 + 1/2 * I * w2

where
M is the mass of the object
V is the speed of the object
I is the moment of inertia of the object
w is the rate of rotation in radians per time

The first term is from the translation(linear motion) of the center of mass and the second term is from the rotation around the center of mass. The moment of inertia is basically a measure of mass distribution times distance squared from the center of rotation. if the moment of inertia is reduced then the ball will spin more with a higher revolution rate.

In the no-slip rolling case w = V / R where R is the radius of the object about its axis rotation. kinetic energy in the no-slip rolling case can be expressed as

KE = 1/2 * M (1 + B) * V2.

B = I / (M * R2).

B is a measure of how compact the mass is to the rotation axis.
For a sphere of uniform density B = 2/5. What this expression of kinetic energy shows is that energy is split between rotation and translation according to the value of B -- which is always less than one.

By making the bowling ball out of a core and and outer shell versus a solid object of uniform density, the size of the ball can be regulated to conform to some regulation size more easily and the moment of inertia can be greater reduced. With a B value less than 2/5 more energy is in translation and the bowling ball will have greater speed. The transfer of momentum from the bowling ball to the pins is almost completely independent on the rotation of the ball since the ball and pins. So a faster moving ball will tend to scatter pins better. Bowlers would call this "better pin carry."

Almost all cores are designed to be asymmetric in distribution of mass. Most cores are shapes like cones or yo-yos with different sized disks. This asymmetric design creates an imbalance in the weight distribution of the bowling ball which gives it a prefered axis of rotation. This axis is usually set mostly perpendicular to the line from the center of the ball to the location of the finger holes. This is to encourage the ball to spin end over end upon release and when going from sliding to rolling.

Most bowlers throw the ball with a hook. A hook is a curve from side rotation, so that a right handed bowler will throw a ball that moves from right to left. The core can be designed to enhance or lessen the natural hook of a bowler. The above explanation should help one read the following bowling ball marketing information or any other sales pitch

http://www.acrossthelanes.com/columns/pp398tw.html

Sincerely,

Tom "Gutter Ball Turkey" Cull


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