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
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.
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