Dünner Stab
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".
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
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.
Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Zeigen Sie dass das Trägheitsmoment J eines dünnen Stabes mit der Drehachse durch das Ende des Körpers und senkrecht zur Körperachse vgl. Abb. gegeben ist als: J fracml^ falls die Gesamtmasse des Stabes m und die Länge l sind. Nehmen Sie das Trägheitsmoment J_Sfracml^ eines dünnen Stabes mit der Drehachse durch den Schwerpunkt und senkrecht zur Körperachse als gegeben an. center tikzpicturescale % Achsen draw thick - -- node right J_S fracml^; draw thick - -- node right J fracml^; % Pfeil draw - .. -- node right ? ..; % Zylinder filltop colorgray!!blackbottom colorgray!middle colorgrayshadingaxisopacity. circle .cm and .cm; fillleft colorgray!!blackright colorgray!!blackmiddle colorgray!shadingaxisopacity. . -- . arc ::.cm and .cm -- -. arc ::.cm and .cm; filltop colorgray!!bottom colorgray!middle colorgray!shadingaxisopacity. circle .cm and .cm; draw -. -- -. arc ::.cm and .cm -- . ++ -. circle .cm and .cm; node right at .. l; tikzpicture center
Solution:
Die Lösung ist mit dem Satz von Steiner sehr einfach. Es gilt nämlich: J J_S + ma^ wobei a der Abstand der Drehachsen ist also hier a fracl. Damit erhalten wir: J fracml^ + mleftfraclright^ leftfrac + fracrightml^ fracml^.
Zeigen Sie dass das Trägheitsmoment J eines dünnen Stabes mit der Drehachse durch das Ende des Körpers und senkrecht zur Körperachse vgl. Abb. gegeben ist als: J fracml^ falls die Gesamtmasse des Stabes m und die Länge l sind. Nehmen Sie das Trägheitsmoment J_Sfracml^ eines dünnen Stabes mit der Drehachse durch den Schwerpunkt und senkrecht zur Körperachse als gegeben an. center tikzpicturescale % Achsen draw thick - -- node right J_S fracml^; draw thick - -- node right J fracml^; % Pfeil draw - .. -- node right ? ..; % Zylinder filltop colorgray!!blackbottom colorgray!middle colorgrayshadingaxisopacity. circle .cm and .cm; fillleft colorgray!!blackright colorgray!!blackmiddle colorgray!shadingaxisopacity. . -- . arc ::.cm and .cm -- -. arc ::.cm and .cm; filltop colorgray!!bottom colorgray!middle colorgray!shadingaxisopacity. circle .cm and .cm; draw -. -- -. arc ::.cm and .cm -- . ++ -. circle .cm and .cm; node right at .. l; tikzpicture center
Solution:
Die Lösung ist mit dem Satz von Steiner sehr einfach. Es gilt nämlich: J J_S + ma^ wobei a der Abstand der Drehachsen ist also hier a fracl. Damit erhalten wir: J fracml^ + mleftfraclright^ leftfrac + fracrightml^ fracml^.
Meta Information
Exercise:
Zeigen Sie dass das Trägheitsmoment J eines dünnen Stabes mit der Drehachse durch das Ende des Körpers und senkrecht zur Körperachse vgl. Abb. gegeben ist als: J fracml^ falls die Gesamtmasse des Stabes m und die Länge l sind. Nehmen Sie das Trägheitsmoment J_Sfracml^ eines dünnen Stabes mit der Drehachse durch den Schwerpunkt und senkrecht zur Körperachse als gegeben an. center tikzpicturescale % Achsen draw thick - -- node right J_S fracml^; draw thick - -- node right J fracml^; % Pfeil draw - .. -- node right ? ..; % Zylinder filltop colorgray!!blackbottom colorgray!middle colorgrayshadingaxisopacity. circle .cm and .cm; fillleft colorgray!!blackright colorgray!!blackmiddle colorgray!shadingaxisopacity. . -- . arc ::.cm and .cm -- -. arc ::.cm and .cm; filltop colorgray!!bottom colorgray!middle colorgray!shadingaxisopacity. circle .cm and .cm; draw -. -- -. arc ::.cm and .cm -- . ++ -. circle .cm and .cm; node right at .. l; tikzpicture center
Solution:
Die Lösung ist mit dem Satz von Steiner sehr einfach. Es gilt nämlich: J J_S + ma^ wobei a der Abstand der Drehachsen ist also hier a fracl. Damit erhalten wir: J fracml^ + mleftfraclright^ leftfrac + fracrightml^ fracml^.
Zeigen Sie dass das Trägheitsmoment J eines dünnen Stabes mit der Drehachse durch das Ende des Körpers und senkrecht zur Körperachse vgl. Abb. gegeben ist als: J fracml^ falls die Gesamtmasse des Stabes m und die Länge l sind. Nehmen Sie das Trägheitsmoment J_Sfracml^ eines dünnen Stabes mit der Drehachse durch den Schwerpunkt und senkrecht zur Körperachse als gegeben an. center tikzpicturescale % Achsen draw thick - -- node right J_S fracml^; draw thick - -- node right J fracml^; % Pfeil draw - .. -- node right ? ..; % Zylinder filltop colorgray!!blackbottom colorgray!middle colorgrayshadingaxisopacity. circle .cm and .cm; fillleft colorgray!!blackright colorgray!!blackmiddle colorgray!shadingaxisopacity. . -- . arc ::.cm and .cm -- -. arc ::.cm and .cm; filltop colorgray!!bottom colorgray!middle colorgray!shadingaxisopacity. circle .cm and .cm; draw -. -- -. arc ::.cm and .cm -- . ++ -. circle .cm and .cm; node right at .. l; tikzpicture center
Solution:
Die Lösung ist mit dem Satz von Steiner sehr einfach. Es gilt nämlich: J J_S + ma^ wobei a der Abstand der Drehachsen ist also hier a fracl. Damit erhalten wir: J fracml^ + mleftfraclright^ leftfrac + fracrightml^ fracml^.
Contained in these collections: