The moment of inertia (MoI) for a water bottle rolling down an inclined ramp is not simply defined by the formulas for a hollow cylinder (I = mr²) or a solid cylinder (I = ½mr²). The actual MoI will vary based on the bottle's geometry, including the neck and base design, as well as the thickness of the material. When the bottle contains water, the interaction between the water and the bottle complicates the MoI further, as the water does not rotate uniformly with the bottle. Therefore, the MoI for a water bottle will lie between the two standard formulas, depending on its specific characteristics.
PREREQUISITESPhysics students, mechanical engineers, and anyone interested in understanding the dynamics of rolling objects, particularly in the context of fluid-filled containers.
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.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?
There is a difference between a water bottle and a bottle of water. The former may or may not contain water.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.