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.
The moment of inertia for a water bottle depends on its shape and size. It is a measure of how difficult it is to rotate the bottle around its axis. This value is usually calculated experimentally or using mathematical formulas.
The moment of inertia can be calculated by integrating the mass of the water bottle with respect to its distance from the axis of rotation. The formula for calculating moment of inertia varies depending on the shape of the bottle. For a cylindrical water bottle, the formula is I = 1/2 * m * r^2, where m is the mass of the bottle and r is the radius.
Yes, the material of the water bottle can affect its moment of inertia. Objects with larger mass and greater distance from the axis of rotation have a higher moment of inertia. Therefore, a water bottle made of a denser material will have a higher moment of inertia compared to a lighter material.
The shape of the water bottle directly affects its moment of inertia. Objects with a larger radius have a higher moment of inertia, as the mass is distributed at a greater distance from the axis of rotation. This is why a cylindrical water bottle will have a higher moment of inertia compared to a spherical water bottle with the same mass.
The moment of inertia is important for a water bottle because it affects how the bottle will behave when it is rotated or spun. It is a key factor in understanding the stability and motion of the bottle. A higher moment of inertia means that more force will be required to rotate the bottle, making it more difficult to change its direction or speed.