Circular motion of a bucket filled with water

[Chestermiller]

Does anyone else besides me feel like this thread is going down the rabbit hole?

 

[jbriggs444]

When there is a vertical motion with an object connected to the centre by an extensible string, there are varying magnitudes of tension at each point because of the change in centripetal force. What I am asking is whether this situation could give rise to an angular acceleration?

What do you mean by an "extensible string"? Do you still envision a circular path? Do you still envision a circular path centered on the attachment point of the string? Where along the path do you expect angular acceleration to occur?

 

[Faiq]

What do you mean by an "extensible string"? Do you still envision a circular path? Do you still envision a circular path centered on the attachment point of the string? Where along the path do you expect angular acceleration to occur?

What I mean by an extensible string is the amount of tension in the string is significant enough to cause an extension which will result in varying values of radius. As a result, an elliptical motion will be generated.
I want to know whether at any point will angular acceleration occur in such a case.

 

[jbriggs444]

What I mean by an extensible string is the amount of tension in the string is significant enough to cause an extension which will result in varying values of radius. As a result, an elliptical motion will be generated.
I want to know whether at any point will angular acceleration occur in such a case.

You have not specified how the central force varies with string extension. That affects string length which, in turn, affects angular velocity and angular acceleration. Chet seems to have the right idea. There is little point in pursuing this line of inquiry.

 

[Chestermiller]

This problem has gotten way too complicated way too fast. It violates the three most important rules about modeling:

1. Keep it simple
2. Keep it simple
3. Keep it simple

Because of inexperience, @Faiq has greatly underestimated the complexity of a problem with a (deformable) fluid in the bucket (which would involve complicated fluid mechanics inside the bucket) and an elastic rope. So we need to take some steps back. Let's start out by analyzing the following two simpler problems:

1. A rigid mass attached to an inextensible string moving in a circle. The bucket is replaced by the rigid mass. The center of the circle remains fixed and dissipative effects are negligible. So the motion will go on forever. What is the tangential velocity of the mass as a function of angle above the horizontal if the velocity of the mass at the top of the arc is V? What is the tangential acceleration of the mass as a function of the angle?

2. Same as problem 1, except with a string that obeys Hooke's law.

Go to it @Faiq.

Chet

 

[Faiq]

Yes Thank you for modelling my query as a formal physics question.