Thanks to the good engineers at Virginia Tech for the content.
Moments of inertia is one of those abstract things learned in kinematics. Understanding things going up and down and friction is easy, but this requires a bit of a step
Formally, a moment of inertia is usually represented by the letter I. For inertia? I'm not really sure. Anyways, here's the formula:$$I=\sum_{i=1}^Nm_ir_i^2$$It is interesting (and relevant to this example) to note that this formula depends on the axis of rotation. This axis isn't always obvious, but here it is along the crane, specifically where it flips over.
There are two reasons that the crane would flip. The first is if the center of mass of the object is outside of the base (anyone who has tried to balance something on end understands this, at least qualitatively). In the third picture, however, the car is out of the water and the crane, while leaning, seems to be doing generally alright.
The other potential problem has to do with applying a force out at a distance. The math here is unnecessary for our purposes, but basically the farther away the car is from the axis of rotation, and the heavier the car weighs in addition to how hard the crane is pulling, needs to be effectively "balanced out" by the rest of the crane. The calculation for this involves the moment of inertia of the whole crane. Needless to say, this is something that any good crane operator should be aware of.
That's moments.
No comments:
Post a Comment