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I am currently studying Kinematics and there's a little bit confusion about the definition of point object given in my course book NCERT(it is a standard textbook in India) which is as follows :

This approximation (of point object) is valid so far as the size of the object is much smaller than the distance it moves in a reasonable duration of time.

But when I started solving the exercise, one particular question requires the learner to differentiate weather an object in a particular situation can be considered as point objects or not and there are two options which cannot (as far as I think) be differentiated into any of these categoriea by considering the definition, which are :

(c) a spinning cricket ball that turns sharply on hitting the ground.

(d) a tumbling beaker that has slipped off a table.

Please give an proper and elaborated definition of point object and also the usage of this approximation in physics.

Also, please clarify the advantages of this definition.

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    $\begingroup$ Well, what do you think? Do you think the objects in your questions should or should not be considered to be point objects? Why or why not? Also, your question needs to be focused on a single question. Right now you have two or three questions. What is a point object? Are these things considered point objects? and What is the advantage of point objects? Please edit your question to just focus on a single inquiry. $\endgroup$ – Aaron Stevens Aug 20 '19 at 15:34
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A point is mathematically dimensionless.The definition given in your textbook is a good(not the best) approximation.

Advantages

This definition allows us to be carefree about a degree of freedom I.e. rotation about it's own axis which simplifies most of problems the beginners tackle in the early stage of learning.

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First of all, the thing you quoted as definition of point object is a statement of when this concept of assuming real world objects to be point objects becomes useful. Point object is an object without dimensions. No real world macroscopic object can satisfy this definition, but when it's too small we can consider it to be point. The word small here is relative, so even a car can be considered point when it's covering kilometers of distance. That's what written in your book.

Now coming on examples. In the first one, you can take ball to be point if it's thrown across the field but points don't rotate, and so can't make sharp turns. Hence here you should not consider it as point object. In second case, it depends on the size of beaker and the height of table.

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