What is the moment of inertia for a water bottle?

Click For Summary

Discussion Overview

The discussion revolves around determining the moment of inertia for a water bottle rolling down an inclined ramp, considering different conditions such as whether the bottle is empty or filled with water. Participants explore the implications of the bottle's geometry and contents on its moment of inertia.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that for an empty bottle, the moment of inertia could be close to ##mr^2##, while for a filled bottle, the situation is more complex due to the interaction between the water and the bottle.
  • Another participant argues that the moment of inertia cannot be simply defined without more information about the specific type of bottle, as it is not an idealized cylinder.
  • A different viewpoint emphasizes that the moment of inertia for a real bottle will be somewhere between that of a hollow cylinder and a solid rod, influenced by the bottle's geometry and thickness.
  • Some participants note that the concept of moment of inertia may not apply straightforwardly to a water bottle due to the lack of unambiguous rotation rates when water is involved.
  • There is a distinction made between a water bottle and a bottle of water, indicating that the contents significantly affect the analysis.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the moment of inertia of a water bottle, and the discussion remains unresolved with no consensus on a definitive answer.

Contextual Notes

Participants highlight limitations in defining the moment of inertia due to the dependence on the specific geometry of the bottle and the conditions of its contents, which are not fully specified.

phuntimes
Messages
1
Reaction score
0
Hi, I'm setting up an equation for initial gravitational potential energy, and I'm just wondering what the moment of inertia, I, would be for a water bottle rolling down an inclined ramp?

Is it mr2 or ½mr2

Or would it be something else?
 
Physics news on Phys.org
If the bottle is empty, it will be close to ##mr^2##. See the item here for 'thin cylindrical shell with open ends'.

But if the bottle contains water, whether completely or only partially full, it will be much more complicated. The water will mostly not rotate as the bottle rolls down. But there will be friction between the water and the bottle, which will cause some of the water to rotate, as well as generating heat and acting as a brake. I expect the rate of rolling would be somewhere between that for an object with MoI= ##mr^2## and one with MoI = ##\frac12 mr^2##.
 
  • Like
Likes   Reactions: phuntimes
Neither. A water bottle generally is not an idealised cylinder. It will depend a lot on the type of bottle and it is just impossible to give any sort of reasonable answer without more information.
 
phuntimes said:
Hi, I'm setting up an equation for initial gravitational potential energy, and I'm just wondering what the moment of inertia, I, would be for a water bottle rolling down an inclined ramp?

Is it mr2 or ½mr2

Or would it be something else?
Those two formulae refer to A hollow cylinder and A solid rod. Once you have realized what those two formulae actually refer to (and why), the whole thing should become clear. The answer will be somewhere in between for a real bottle. The geometry of the neck and the base will affect the value, too and so would the thickness of the envelope.
P.S. You can ADD moments of inertia.
 
Moment of inertia is a useful concept for bodies that rotate rigidly and accordingly have an unambiguous rotation rate. A bottle of water does not qualify.
 
jbriggs444 said:
Moment of inertia is a useful concept for bodies that rotate rigidly and accordingly have an unambiguous rotation rate. A bottle of water does not qualify.
There is a difference between a water bottle and a bottle of water. The former may or may not contain water.
 

Similar threads

High School Inertia of a rolling dumbell
  • · Replies 2 ·
Replies
2
Views
1K
High School Why does torque increase with increasing moment of inertia?
  • · Replies 13 ·
Replies
13
Views
2K
High School Rotational Dynamics: Confused about the tension in this string pulling a mass up an incline
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How can I calculate the moment of inertia of any object?
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Torque and Moment of Inertia of a Lever Arm
  • · Replies 2 ·
Replies
2
Views
4K
Moment of Inertia with pulley and two masses on a string (iWTSE.org)
  • · Replies 8 ·
Replies
8
Views
15K
Undergrad Experimental determination of the moment inertia of a sphere
  • · Replies 2 ·
Replies
2
Views
2K
High School What sort of can would roll the fastest?
  • · Replies 12 ·
Replies
12
Views
8K
Calculating Moment of Inertia for Hollow Cylinder w/ Water
  • · Replies 40 ·
2
Replies
40
Views
6K
Undergrad How To Create the Fastest Rolling Can Possible
  • · Replies 13 ·
Replies
13
Views
6K