is not quite constant, but close enough.
You're right, varying the mass of the bob (ball) in the usual pendulum model won't affect the period or speed of it. However, the normal pendulum model is not applicable in this situation.
What you're thinking of is the model where the ball is attached to a weightless string, the entire mass of the system is contained in the ball. The period is related to sqrt(l
), where l
is the length of the pendulum arm. Longer arms means more speed because the ball has more gravitational potential energy (it "falls" from a greater height). The mass of the object is irrelevant.
However, my arms have mass, unlike the arm in the simple model. The "length" of the pendulum is not simply my arm's length, it's the center of mass of the arm/ball system. Probably going to be somewhere in my forearm. A heavier ball will pull the center of mass towards the ball, a lighter ball will pull it towards the elbow. Hence, with a heavier ball, the pendulum arm is actually longer. Longer pendulum arm means that the actual end of my arm is moving faster.
But that ignores a lot of things. For one, even the free-est of swings is not truly free. We all put some muscle into the ball, and lighter weight balls are simply easier to muscle. Second, it ignores the fact that foot speed affects ball speed. You can't run up to the line as quickly with a heavier ball, your legs have to compensate for the ball's inertia as you swing it behind you. A heavier ball has more inertia and to keep the ball moving with your body, you have to hold it tighter, lest the ball flies back into the pit. That tighter grip means more muscling of the ball. Third, that typical pendulum model is not a good approximation of your arm with a bowling ball stuck on the end that swings over a wide range of motion in which even the fulcrum is moving.
Bottom line is to throw what's comfortable. You can't assume that a heavier or lighter ball will give you more speed, there are simply too many variables that are unique to your body that classical, simple physics doesn't take into account. Your carry will be best when you are comfortable and are bowling with the optimum amount of effort. There are tradeoffs all around: Does going up in weight make you more speed- or rev-dominant? Does your speed change more than the revs you're getting? In which way? Can you swing the ball more and generate more angle because you're now rev-dominant? Do you tend to drop the ball or have a weak release because it's too heavy? Are you blowing past the breakpoint?
There is some handwaving, but in all physical endeavors, what works for one may not work for another, no matter what the over-simplified, not-actually-applicable, gedanken model says. There are modeling errors
that affect different people in different ways.
Plus, a heavier object does generate more force (F=ma), just not more speed.
Edited on 10/29/2007 9:33 AM