Moment of inertia of an object with uneven distribution of weight

In summary, for an experiment involving calculating the rotational kinetic energy of a can rolling down an inclined plane, the equation Er=1/2Iw^2 is used. However, the equation I=mr^2 only applies when the weight is evenly distributed throughout the axis. In order to calculate the moment of inertia in an experiment where mass is only added to one side of an empty cylindrical can, the general formula I=\int r^{2} dm must be used. It may be beneficial to distribute the added mass in a way that simplifies the integral.
  • #1
sungj25
3
0
I'm doing an experiment and I have to calculate calculate rotational kinetic energy of this can rolling down an inclined plane.
According to the equation, Er=1/2Iw^2, I=mr^2, and w=v/r (no slipping effect) right?
but doesn't I=mr^2 apply only when the weight is evenly distributed throughout the axis?

In my experiment, I'm going to add mass only on one side of an empty cylindrical can (using bluetag). Will I be still able to calculate the inertia using this I=mr^2 equation?

thank you for reading!
 
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  • #2
The general formula for calculating the moment of inertia of a body about an axis is:

[itex]I=\int r^{2} dm[/itex]

where r represents the distance of the mass element from the rotational axis. If the distance from the axis is so large that the distribution of the mass becomes negligible, then the formula you mention (mr2) is applicable. (for example the moment of inertia of the Earth about the sun).

For your experiment you will need to use the general formula to account for the manner in which you distribute your bluetag. You might want to distribute the bluetag in a manner to simplify the integral.
 

FAQ: Moment of inertia of an object with uneven distribution of weight

1. What is moment of inertia?

Moment of inertia is a measurement of an object's resistance to rotational motion. It is influenced by the mass and distribution of weight of an object.

2. How is moment of inertia calculated?

Moment of inertia is calculated by multiplying the mass of each individual particle of an object by the square of its distance from the axis of rotation and then summing all of these values together.

3. How does uneven distribution of weight affect moment of inertia?

An uneven distribution of weight in an object will result in a larger moment of inertia compared to an object with a more even distribution of weight. This is because the particles further from the axis of rotation contribute more to the moment of inertia.

4. What is the significance of moment of inertia?

The moment of inertia is an important concept in physics and engineering, as it helps determine an object's stability, rotational acceleration, and resistance to changes in rotational motion.

5. How is moment of inertia used in real-world applications?

Moment of inertia is used in various real-world applications such as designing structures, calculating the performance of rotating machines, and understanding the motion of celestial bodies. It is also important in sports such as figure skating, diving, and gymnastics, where it affects an athlete's ability to rotate and maintain balance.

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