The drawing shows three objects rotating about a vertical axis. The mass of each object is given in terms of m0, and its perpendicular distance from the axis is specified in terms of r0. Rank the three objects according to their moments of inertia, largest to smallest.
The answer is A, then C, then B
wtf, bobpursley is absolutely correct; moreover, it's simple af to just solve through using the formula bob gave, bunch of idiots only wants answers instead of learning
To rank the three objects according to their moments of inertia, we need to understand what moment of inertia is. The moment of inertia, denoted by I, quantifies how an object resists rotational motion about a particular axis. It depends on both the mass distribution of the object and the location of this axis of rotation.
In this case, since the objects are rotating about a vertical axis, we can use the formula for the moment of inertia of a point mass:
I = m * r^2
Where:
- I is the moment of inertia
- m is the mass of the object
- r is the perpendicular distance from the axis of rotation to the mass
Let's label the three objects as A, B, and C, with A having the largest mass and being farthest from the axis of rotation, and C having the smallest mass and being closest to the axis of rotation.
Based on the formula, we can deduce that the larger the mass and the farther the mass is from the axis of rotation, the larger the moment of inertia will be.
Therefore, we can rank the objects as follows, from largest to smallest moment of inertia:
1. Object A: It has the largest mass and is farthest from the axis of rotation.
2. Object B: It has a smaller mass than Object A but is still farther from the axis of rotation than Object C.
3. Object C: It has the smallest mass and is closest to the axis of rotation.
Remember, the moment of inertia is directly proportional to the mass and the square of the distance from the axis of rotation.
moment of inertia for each mass is
mr^2
compute each, then rank them. Goodness.