Physics Question: Spin & Tip Offset

[Patrick Johnson]

Does spin increase linearly or exponentially with tip offset? Does the last mm of tip offset add more spin than the first one did?

Thanks,

pj
chgo

 

[worriedbeef]

hmmm this has got the rusty cogs in my brain spinning.

do you mean is the difference between the amount of spin between say the final two mm's of tip offset more than the difference between the first two mm's of tip offset?

if so i would say yes, because that's the nature of a sphere. but to be honest my brain is in overdrive trying to fully comprehend the question.

 

[Franky]

Torque = r x F

so I'd have to say linearly (ignoring the little stuff that is...)

 

[LoGiC]

From an engineer's point of view:

Increases linearly,

the out most portion of the tip does add more spin than the inner most (in relation to cue ball center.

 

[Jal]

Does spin increase linearly or exponentially with tip offset? Does the last mm of tip offset add more spin than the first one did?

Thanks,

pj
chgo

Pat,

To add to what the other posters have said.

To a very good approximation the spin/speed ratio increases linearly with offset. To some extent though, the last mm of offset should add more than the first one because of the greater average ball rotation rate during impact, but not much. And this is opposed somewhat by greater squirt which decreases the effective offset. Linear is good for figuring things.

I can't say that I've taken measurements to verify theory, or read of such, but the fact that you can spin a ball faster than its natural roll rate suggests that the theory is pretty close. And it is pretty simple as far as the linear part is concerned.

Absolute spin rate doesn't increase linearly with offset, however. It doesn't increase as fast because ball speed drops off with tip offset, ie, energy gets put into spin.

Jim