Why is it easier to balance a long pole (like a broom handle) on my palm that it is to balance a short stick on my palm?
In: 68
More mass AND further away makes it hard to start tipping and falling… It’s called “moment of inertia”…. Even if the weight was the same, if it further away from the pivot, it takes way more force to start moving
It’s exactly like a pendulum, but upside down. The farther the distance of the center of mass is from the fulcrum, the more slowly it will swing (the longer it’s moment).
Angles. If the tip of a short stick moves one inch, it may be a 25° difference. If the tip of a long stick moves one inch, it could be only 2° or so. It takes more movement for the center of mass to pass the tipping point.
Imagine a large ball with a stick poking out out of the bottom. If the stick points straight down, it will balance.
If the stick is at an angle where the bottom of the stick is further to the side than the edge of the ball, it will definitely fall over.
If the stick is short, the end can be moved past the edge of the ball really quickly and the stick will be at a pretty extreme angle. If it’s long it takes a bit longer to move past the edge and the stick will only have a small angle.
The long stick, means you can make small slower adjustments to keep the end of the stick under the ball and keep it balanced.
With a short stick, when it becomes unbalanced, the angle of the stick is so great, you have to make big movements to try and bring it back, which makes it really easy to over correct and make it worse.
So a long stick gives you much finer control and more forgiving to overcorrection. The same amount of movement the puts the long stick at an angle of only a few degrees off vertical, will put a short stick close to horizontal.
There is more to it, but this is the best ELI5 I can come up with.
The amount of room for error is expanded the longer something is. I don’t know the physics but it works the same with backing up trailers. The longer they are the easier it is to back up.
I’m dumb but this is what I think is happening.
To make the analysis easier we should start with this.
1. Assume that long and short rods are uniformly cylindrical shaped.
2. That the more the center of mass deviates from the point of support(where the rod touches the palm of the hand) the more unstable the system is.
More unstable=The rod is harder to balance and fall
Center of mass= the location/point in an object at which the mass can be represented.
Center of mass for a rod = 1/2 the rod’s length
So what generally happens during balancing a rod is
1. You can barely notice the movement of the rod
2. Multiple disturbances are happening in the rod that causes it to fall
3. You are moving the base of the rod to follow the center of mass of the rod and balance the system.(I will not delve deeper but moment also happens here)
4. There is an angle formed with respect to the base of the rod when it starts to lean
Since we can’t really measure the amount of force we apply to balance the rod and are limited with what force we can exert we can just assume that there should be a minimum angle at which the human force will not be enough and the rod will fall.
So we have the following:
1. Minimum angle before fall
2. Center of mass of long rod and short rod
Answer: To simplify this, imagine 2 slices of pizza with different radius but with the same angle such that the slices perfectly overlap with each other.
In this example we can say that
1. Angle of pizza-minimum angle before fall
2. Center of mass for short and long rod will be the radius of the pizza
3. Crust length= distance traveled by the center of mass from the base
As you can notice that the slice of pizza with higher radius has relatively higher crust length which means the center of can travel much further without exceeding the minimum angle.
In reality,
1. The minimum angle is much much smaller than the slice of pizza.
2. The rod can fall in any direction
3. Our palms are not that sensitive and there is a delay from the sensor and brain to send signals to hand for correction.
In short, bigger pizza radius= linger crust length= give us enough time to sense think and react to balance the unstable rod.
I’m wrong at many points here feel free to correct me.
This is also why in Kerbal Space Program, you want your upper stages to have a decent amount of mass to them. Otherwise if you have a fat 1st stage, it is too easy for your rocket to flip over and lose control. Fins help, but only a little.
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