A cue ball is travelling along a snooker table. Initially, it has only side spin (yaw). As it travels it will develop a rolling spin (pitch).

Can the ball develop any (roll) and thus move off the initial linear trajectory?

My maths knowledge says no, but my physics is rather poor.

Physically, this would be equivalent to playing the perfect side spin shot (perfectly flat cue through the horizontal equator)

Thanks in advance for any help.


Yes it moves sideways, in the direction of the side spin. The spin momentum interact with the newly imposed pitch, resulting on longitudinal spin (rotating along main direction) that make the ball deviate. See for example Wikipedia

Another effect is the interaction with air; a rotating ball tend to curve its trajectory toward rotation side, as done in "spin" shots in baseball and tennis. Bit I will say that is weak in billiard.

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  • $\begingroup$ Will the ball follow an arc or will it balance itself onto a new straight trajectory? When I play a ball with sidespin along the diagonal of a snooker table, I can make the ball go from pocket to pocket without deviation (with sidespin). Am I accounting for the initial change in linear trajectory or is the arc effect so small that it is negligible? $\endgroup$ – Ben Crossley Apr 11 '19 at 9:58
  • $\begingroup$ With the momentum caused by interaction of spin and rolling, it should curve at the beginning (when it acqires roll) then stabilize to straight trajectory, while still having strong spin. Like when the ball goes straight, but when it bounces against the side takes an odd angle thanks to the spin. For the interaction with air, it should deviate all the way, until has spin. Another effect may be the with contact with the table, the friction from spin can give some thrust $\endgroup$ – patta Apr 11 '19 at 11:16

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