Trägheitsmoment einer Pyramide
About points...
We associate a certain number of points with each exercise.
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But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
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.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
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 -
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 -
Question
Solution
Short
Video
\(\LaTeX\)
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The following quantities appear in the problem:
Länge \(\ell\) / Masse \(m\) / Volumen \(V\) / Fläche \(A\) / Höhe \(h\) / Trägheitsmoment \(J, \Theta, I\) / Radius \(r\) / Dichte \(\varrho\) /
The following formulas must be used to solve the exercise:
\(\varrho = \dfrac{m}{V} \quad \) \(V = \dfrac13 A h \quad \) \(J = \int r^2 \, \text{d}m \quad \) \(J = \dfrac{1}{10}ma^2 \quad \)
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Exercise:
Berechne das Trägheitsmoment einer regelmässigen Pyramide mit Masse m der Höhe h und einer quadratischen Grundfläche mit Seitenlänge a bezüglich ihrer Symmetrieachse.
Solution:
Das Trägheitsmoment einer regelmässigen Pyramide mit einer quadratischen Grundfläche mit Seitenlänge a und einer Höhe h berechnet man folgermassen: J _m r^mboxdm _V r^rhomboxdV rho _x_y_z x^+y^ mboxdx mboxdy mboxdz rho _^hmboxdz_-b^bmboxdy_-b^bmboxdx x^+y^ && b fracazh rho _^hmboxdz_-b^bmboxdyleftfracx^+xy^right_-b^b rho _^hmboxdz_-b^bmboxdyleftfracb^+by^right rho _^hmboxdzleftfracb^y+frac by^right_-b^b rho _^hmboxdzleft frac b^ + frac b^right rho _^hmboxdz frac b^ && fracbz fracfracah rho _^hmboxdz frac leftfracahzright^ rho fraca^h^ leftfrac z^right_^h rho fraca^h^ frac h^ rho fraca^ h rho frac a^ h frac a^ frac ma^
Berechne das Trägheitsmoment einer regelmässigen Pyramide mit Masse m der Höhe h und einer quadratischen Grundfläche mit Seitenlänge a bezüglich ihrer Symmetrieachse.
Solution:
Das Trägheitsmoment einer regelmässigen Pyramide mit einer quadratischen Grundfläche mit Seitenlänge a und einer Höhe h berechnet man folgermassen: J _m r^mboxdm _V r^rhomboxdV rho _x_y_z x^+y^ mboxdx mboxdy mboxdz rho _^hmboxdz_-b^bmboxdy_-b^bmboxdx x^+y^ && b fracazh rho _^hmboxdz_-b^bmboxdyleftfracx^+xy^right_-b^b rho _^hmboxdz_-b^bmboxdyleftfracb^+by^right rho _^hmboxdzleftfracb^y+frac by^right_-b^b rho _^hmboxdzleft frac b^ + frac b^right rho _^hmboxdz frac b^ && fracbz fracfracah rho _^hmboxdz frac leftfracahzright^ rho fraca^h^ leftfrac z^right_^h rho fraca^h^ frac h^ rho fraca^ h rho frac a^ h frac a^ frac ma^
Meta Information
Exercise:
Berechne das Trägheitsmoment einer regelmässigen Pyramide mit Masse m der Höhe h und einer quadratischen Grundfläche mit Seitenlänge a bezüglich ihrer Symmetrieachse.
Solution:
Das Trägheitsmoment einer regelmässigen Pyramide mit einer quadratischen Grundfläche mit Seitenlänge a und einer Höhe h berechnet man folgermassen: J _m r^mboxdm _V r^rhomboxdV rho _x_y_z x^+y^ mboxdx mboxdy mboxdz rho _^hmboxdz_-b^bmboxdy_-b^bmboxdx x^+y^ && b fracazh rho _^hmboxdz_-b^bmboxdyleftfracx^+xy^right_-b^b rho _^hmboxdz_-b^bmboxdyleftfracb^+by^right rho _^hmboxdzleftfracb^y+frac by^right_-b^b rho _^hmboxdzleft frac b^ + frac b^right rho _^hmboxdz frac b^ && fracbz fracfracah rho _^hmboxdz frac leftfracahzright^ rho fraca^h^ leftfrac z^right_^h rho fraca^h^ frac h^ rho fraca^ h rho frac a^ h frac a^ frac ma^
Berechne das Trägheitsmoment einer regelmässigen Pyramide mit Masse m der Höhe h und einer quadratischen Grundfläche mit Seitenlänge a bezüglich ihrer Symmetrieachse.
Solution:
Das Trägheitsmoment einer regelmässigen Pyramide mit einer quadratischen Grundfläche mit Seitenlänge a und einer Höhe h berechnet man folgermassen: J _m r^mboxdm _V r^rhomboxdV rho _x_y_z x^+y^ mboxdx mboxdy mboxdz rho _^hmboxdz_-b^bmboxdy_-b^bmboxdx x^+y^ && b fracazh rho _^hmboxdz_-b^bmboxdyleftfracx^+xy^right_-b^b rho _^hmboxdz_-b^bmboxdyleftfracb^+by^right rho _^hmboxdzleftfracb^y+frac by^right_-b^b rho _^hmboxdzleft frac b^ + frac b^right rho _^hmboxdz frac b^ && fracbz fracfracah rho _^hmboxdz frac leftfracahzright^ rho fraca^h^ leftfrac z^right_^h rho fraca^h^ frac h^ rho fraca^ h rho frac a^ h frac a^ frac ma^
Contained in these collections
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Trägheitsmoment 2 by uz
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Trägheitsmoment Pyramide by TeXercises
| Title | Matched on |
|---|---|
| Trägheitsmoment einer Pyramide | tagstitle |
| Trägheitsmoment von Pyramide | title |
| Trägheitsmoment von Pyramide | title |
| Trägheitsmoment eines Zylinders | title |
| Trägheitsmoment eines Quaders | title |
Similar exercises (9)
| Title | Matched on |
|---|---|
| Trägheitsmoment einer Pyramide | tagstitle |
| Trägheitsmoment von Pyramide | title |
| Trägheitsmoment von Pyramide | title |
| Trägheitsmoment eines Zylinders | title |
| Trägheitsmoment eines Quaders | title |
| Trägheitsmoment einer Kugel | title |
| Trägheitsmoment eines Kegels | tags |
| Trägheitsmoment eines Kegelstumpfes | tags |
| Trägheitsmoment eines inhomogenen Kegels | tags |