“To a first approximation, its behaviour is described by Newton's second law of motion $f=ma$: the force $f$ of the roll equals the ball's mass, $m$, times its acceleration, $a$
“The force of the roll” is such a problem misunderstanding of what a force is it made me stop reading. There is no such thing as the force of the roll. There. An be a force acting on the ball and or a force the ball exerts on something else, but the force is more verblike. It is an interaction between two objects, not the property of one object.

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