My brother told me that household buckets have rims curled outwards to increase their polar moment of inertia.

But for what? This increased moment of inertia is needed to counteract what?

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    $\begingroup$ I think the curled rim is for mechanical stability of the rim. Note that a bucket without the rim cut off has almost no resistance against folding up and is pretty useless. $\endgroup$ – Christian Vögl Feb 2 '17 at 9:53
  • $\begingroup$ I always thought that it is to make the bucket easier to hold, one can put the tip of fingers under the curly part $\endgroup$ – physicopath Feb 2 '17 at 9:56
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    $\begingroup$ Your brother was pulling your leg. $\endgroup$ – Pirx Feb 2 '17 at 12:56
  • $\begingroup$ @Pirx The rim as he told me is a torsion box, he is not pulling my leg, my question is not about buckets, my question is about container ships $\endgroup$ – sofky Feb 2 '17 at 13:20
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    $\begingroup$ The rounded edges I think are there instead (on plastic buckets where they're pronounced and not just to make the rim smooth) to protect against the bowing that takes place when you pick up the bucket by the handle. Both places where the handle touches the rim want to go "up" and "in" and the matter between those contact points will want to go "out" and "down" to compensate. The rigid rim spreads this force out over a larger area to diminish the stress and reduce the effect. That sort of bending is more of a second moment of area type thing, I should think. $\endgroup$ – CR Drost Feb 2 '17 at 15:57

Why have buckets with curved rims?

The polar moment of inertia is used to gauge the capacity of an object to resist twisting, or torsion, (in circular cross sectioned objects). In other words it is a measure of the angular displacement of the bucket when undergoing torque.

So if we filled the bucket with water, and then used the handle to lift it vertically, any slight horizontal motion would cause the bucket walls to twist, and reinforcement of the top by means of a curved rim would possibly reduce this twist, if the handle pivot points were located there on appropriately reinforced areas.

enter image description here

Extract and image from Polar moment of Interia

A schematic showing how the polar moment of area is calculated for an arbitrary shape about an axis $o$.

$ρ$ is the radial distance to the element $dA$.

Definition of polar moment of inertia,

$${\displaystyle I_{z}=\int _{A}\rho ^{2}\,dA}$$ $I_z$ = the polar moment of area about the axis $z$

$dA$ = an elemental area

$ρ$ = the radial distance to the element $dA$ from the axis $z$

For a circular section with radius $r$:

$${\displaystyle I_{z}=\int _{0}^{2\pi }\int _{0}^{r}\rho ^{2}\rho \,d\rho \,d\phi ={\frac {\pi r^{4}}{2}}} $$

Two other advantages , with respect to plastic and other thin walled buckets, should also be mentioned .

The curved rim strengthens the plastic bucket and also increases the mass at the top, raising the center of gravity, making it easier to tip it over, (but only slightly).

The curved rim may reduce drips whilst pouring.

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    $\begingroup$ ...and to carry it. $\endgroup$ – lemon Feb 2 '17 at 10:46
  • $\begingroup$ @lemon Often the lip is only a centimetre or two. Not a whole lot of space to grip. Usually a bucket will have a handle for that. $\endgroup$ – JMac Feb 2 '17 at 10:49
  • $\begingroup$ Thank you dear count10 but my query is what is the addition of polar moment of inertia for. $\endgroup$ – sofky Feb 2 '17 at 13:24
  • $\begingroup$ The curved rim may also prevent cutting your hands against a thin metal edge. $\endgroup$ – LLlAMnYP Feb 2 '17 at 15:02

Moment of inertia? The difference of moment of inertia of a bucket with rim curled inwards and outwards is ridiculously small. But even if it was not - nobody cares.

The rim is (usually) curled to reinforce the bucket and to make it safer (you would not cut your hand if the rim is curled).

The rim is curled outwards to make it possible to pour out all the water from the bucket without having to turn it completely upside-down.

  • $\begingroup$ I have d/v your answer, (which is a first for me when answering the same question) but if I am wrong, I would be happy to reverse that. Sorry. $\endgroup$ – user140606 Feb 2 '17 at 16:56
  • $\begingroup$ @Countto10 You caught me, I did not know about the difference between polar moment of inertia and usual moment of inertia. Having read wiki I am now not sure I completely understand the question. Polar moment of inertia is calculated about some axis. Where is this axis in our case? But somehow it turns out that even though I did not understand the question I still think my answer is correct:) The rim is curled to reinforce the bucket and for safety/convenience. It is curled outwards to make it easier to pour out it's contents. $\endgroup$ – lesnik Feb 2 '17 at 18:54
  • $\begingroup$ I did not know about the difference between polar moment of inertia and usual moment of inertia I would love to say, tut, tut, but truth is, I only learnt the difference an hour before you :) I think it's rotation, rather than translation, about the z axis. $\endgroup$ – user140606 Feb 2 '17 at 20:56

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