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Trägheitsmoment einer Halbkugel

About points...

We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
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That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.

About difficulty...

We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise

Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/tragheitsmoment-einer-halbkugel-1/

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Exercise:
Berechne das Trägheitsmoment einer Halbkugel der Masse m und dem Abstand R. Die Achse verläuft durch den Schwerpunkt.

Solution:
newcommandddmboxd newcommandeg op_-fracazh^fracazh Anmerkung: tilde r ist der Abstand von der Drehachse r der Abstand vom Schwerpunkt. I op tilde r^ dd m varrhoop tilde r^ dd V varrhoop x^+y^ dd V varrho op x^+y^ r^sinvarthetadd rdd varphi ddvartheta varrho op r^sin^varthetacos^varphi + r^sin^varthetasin^varphi r^sinvarthetadd rdd varphi ddvartheta varrho op r^sin^varthetacos^varphi + sin^varphi r^sinvarthetadd rdd varphi ddvartheta varrhoop r^sin^varthetadd r dd varphi dd vartheta varrhoop_^R r^dd r op_^piddvarphi op_^fracpisin^varthetaddvartheta varrhoop_^R r^dd r op_^piddvarphi left -cosvartheta+frac cos^varthetaright_^fracpi varrhoop_^R r^dd r op_^piddvarphi left underbraccosfracpi+frac cos^fracpi_text denn cosfracpi + underbracecos-frac cos^_fractext denn cos right fracvarrhoop_^R r^dd r pi fracvarrholeftfracR^right pi frac R^varrho underbracefracpi R^_V boxedfracmR^

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Trägheitsmomente by pw

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Attributes & Decorations

Tags	halbkugel, körper, pam, starrer, trägheitsmoment
Content image
Difficulty	(4, default)
Points	4 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	pw
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