# Does a rolling ball take slower to reach the ground than a dropped non rotating ball from the same height?

I know in a ramp this isn’t true but there, the path is one dimensional.

However, here after the rolling ball goes off of the edge with a certain angular velocity, is the object's angular velocity constant? I think it is constant as no net torque is being produced.

So is it correct to say that a rolling ball and non rolling ball will reach the ground at the same time when pushed off a table at the same time?

• yes, the time of flight would be same for both. Difference would only be in the time it rolls on the ramp – Rishab Navaneet Jun 24 at 8:33

Let's call the falling direction $$z$$ ($$-z$$ to be exact). The rotation of the ball causes a (small) force perpenticular to the moving direction (so some combination of the $$x$$ and $$y$$ direction), due to the difference speed of the air flow to the sides of the ball Magnus effect. As soon as the ball gets velocity components in $$x$$ or $$y$$ direction, the force from the Magnus effect gets a small (positive) $$z$$ component, which hence lowers the gravitational force and the acceleration in $$-z$$ direction.

So no, they would not reach the ground at the same time. The difference depends on the angular velocity of course and will be small, though.