// Numbas version: finer_feedback_settings {"name": "Moment of inertia: semicircle and hole", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "
A value with units marked right if within an adjustable % error of the correct value. Marked close if within a wider margin of error.
", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n right and good_units and right_sign, add_credit(1.0,'Correct.'),\n right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n close and good_units, add_credit(settings['C1'],'Close.'),\n close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "Modify the unit portion of the student's answer by
\n1. replacing \"ohms\" with \"ohm\" case insensitive
\n2. replacing '-' with ' '
\n3. replacing '°' with ' deg'
\nto allow answers like 10 ft-lb and 30°
", "definition": "replace_regex('ohms','ohm',\n replace_regex('\u00b0', ' deg',\n replace_regex('-', ' ' ,\n studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "This fixes the student answer for two common errors.
\nIf student_units are wrong - replace with correct units
\nIf student_scalar has the wrong sign - replace with right sign
\nIf student makes both errors, only one gets fixed.
", "definition": "switch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "Only marked close if the student actually has the right sign.
", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. if correct answer is 100 N and close is ±1%,Find moment of inertia of a shape which requires the use of the parallel axis theorem for a semicircle.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "{geogebra_applet('fqywxznp',{ggbArgs})}
\nDetermine the moment of inertia and radius of gyration of the composite shape with respect to the x- and y-axes knowing that $b$ = {b}, $h$ = {h}, $r_o$ = {r_o}, and $r_i$ = {display(r_i)}.
", "advice": "Number the parts:
\nPart 1 rectangle: $b$ = {b}, $h$ = {h}.
\nPart 2 semicircle: $r_o$ = {r_o}.
\nPart 3 circular hole: $r_i$ = {display(r_i)}.
\nCalculate the areas:
\n$\\begin{align} A_1 &= b h & A_2 &= \\tfrac{1}{2}\\pi r_o^2 &A_3 &= \\pi r_i^2&A&=A_1 +A_2 - A_3\\\\&=\\var{display(A1)} &&=\\var{display(A2)} &&=\\var{display(A3)}&&=\\var{display(A)}\\\\&&\\end{align}$
\nCalculate the moment of inertia with respect to the x-axis.
\n$\\begin{align} \\\\{I_1}_x &= \\tfrac{1}{3} b h^3 \\\\&= \\tfrac{1}{3}( \\var{b})(\\var{h})^3 \\\\&= \\var{display(Ix1)} \\\\\\\\{I_x}_2 &= [\\bar{I} + A d^2]_2\\\\ &= 0.1098 r_o^4 + \\left(\\frac{\\pi r_o^2}{2}\\right) \\left(h + \\frac{4 r_o}{3 \\pi}\\right)^2\\\\&= \\var{display(Ibarx2)} + (\\var{display(A2)}) (\\var{display(d2)})^2\\\\&=\\var{display(Ix2)} \\\\\\\\ {I_x}_3 &= [\\bar{I} + A d^2]_3 \\\\ &= \\frac{\\pi r_i^4}{4} + \\left(\\pi r_i^2\\right) \\left(h \\right)^2\\\\&= \\var{display(Ibarx3)} + (\\var{display(A3)}) (\\var{display(h)})^2\\\\&=\\var{display(Ix3)}\\\\\\\\I_x &= {I_x}_1+{I_x}_2-{I_x}_3\\\\&=\\var{display(Ix1)}+\\var{display(Ix2)}-\\var{display(Ix3)}\\\\&=\\var{display(Ix)}\\end{align}$
\nCalculate the moment of inertia with respect to the y-axis.
\n$\\begin{align} \\\\{I_y}_1 &= \\tfrac{1}{3} h b^3 \\\\&= \\tfrac{1}{3}( \\var{h})(\\var{b})^3 \\\\&= \\var{display(Iy1)} \\\\\\\\{I_y}_2 &= [\\bar{I} + A d^2]_2\\\\ &= \\frac{\\pi r_o^4}{8} + \\left(\\frac{\\pi r_o^2}{2}\\right) \\left(\\frac{b}{2}\\right)^2\\\\&= \\var{display(Ibary2)} + (\\var{display(A2)}) (\\var{display(b/2)})^2\\\\&=\\var{display(Iy2)} \\\\\\\\ {I_y}_3 &= [\\bar{I} + A d^2]_3 \\\\ &= \\frac{\\pi r_i^4}{4} + \\left(\\pi r_i^2\\right) \\left(\\frac{b}{2} \\right)^2\\\\&= \\var{display(Ibary3)} + (\\var{display(A3)}) (\\var{display(b/2)})^2\\\\&=\\var{display(Iy3)}\\\\\\\\I_y &= {I_y}_1+{I_y}_2-{I_y}_3\\\\&=\\var{display(Iy1)}+\\var{display(Iy2)}-\\var{display(Iy3)}\\\\&=\\var{display(Iy)}\\end{align}$
\nCalculate the radius of gyration with respect to the x- and y- axes.
\n$\\begin{align}\\\\k_x &= \\sqrt{\\dfrac{I_x}{A}}&k_y &= \\sqrt{\\dfrac{I_y}{A}}\\\\ &= \\sqrt{\\dfrac{\\var{display(Ix)}}{\\var{display(A)}}}&&= \\sqrt{\\dfrac{\\var{display(Iy)}}{\\var{display(A)}}}\\\\ &= \\var{display(kx)} &&=\\var{display(ky)} \\end{align}$
\n", "rulesets": {}, "extensions": ["geogebra", "quantities"], "variables": {"A3": {"name": "A3", "group": "Area", "definition": "3.14159 r_i r_i", "description": "", "templateType": "anything"}, "A2": {"name": "A2", "group": "Area", "definition": "3.14159 r_o r_o /2", "description": "", "templateType": "anything"}, "A1": {"name": "A1", "group": "Area", "definition": "b h", "description": "", "templateType": "anything"}, "r_i": {"name": "r_i", "group": "Inputs", "definition": "random(1/3, 0.5, 2/3,0.75) r_o ", "description": "", "templateType": "anything"}, "h": {"name": "h", "group": "Inputs", "definition": "qty(random(2..8),units)", "description": "", "templateType": "anything"}, "Iy": {"name": "Iy", "group": "Iy", "definition": "Iy1 + Iy2 - Iy3", "description": "", "templateType": "anything"}, "Ibary2": {"name": "Ibary2", "group": "Iy", "definition": "3.14159 r_o r_o r_o r_o /8", "description": "", "templateType": "anything"}, "Iy2": {"name": "Iy2", "group": "Iy", "definition": "Ibary2 + A2 b/2 b/2", "description": "", "templateType": "anything"}, "Ix2": {"name": "Ix2", "group": "Ix", "definition": "Ibarx2 + A2 d2 d2", "description": "", "templateType": "anything"}, "Ix1": {"name": "Ix1", "group": "Ix", "definition": "b h h h /3", "description": "rectangle
", "templateType": "anything"}, "kx": {"name": "kx", "group": "Ix", "definition": "qty(sqrt(scalar(Ix/A)),units)", "description": "", "templateType": "anything"}, "Ibary3": {"name": "Ibary3", "group": "Iy", "definition": "Ibarx3", "description": "", "templateType": "anything"}, "d2": {"name": "d2", "group": "Ix", "definition": "h + 4 r_o/3/3.14159", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Inputs", "definition": "qty(random(4..12#2),units)", "description": "", "templateType": "anything"}, "ky": {"name": "ky", "group": "Iy", "definition": "qty(sqrt(scalar(Iy/A)),units)", "description": "", "templateType": "anything"}, "Ibarx2": {"name": "Ibarx2", "group": "Ix", "definition": "0.1098 r_o r_o r_o r_o", "description": "", "templateType": "anything"}, "Ibarx3": {"name": "Ibarx3", "group": "Ix", "definition": "3.14159 r_i r_i r_i r_i/4", "description": "", "templateType": "anything"}, "Iy3": {"name": "Iy3", "group": "Iy", "definition": "Ibary3 + A3 b/2 b/2", "description": "", "templateType": "anything"}, "ggbArgs": {"name": "ggbArgs", "group": "Inputs", "definition": "[['A',vector(scalar(b),scalar(h))],['R_o',scalar(r_o)],['R_i',scalar(r_i)]]", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "Area", "definition": "A1 + A2 - A3", "description": "", "templateType": "anything"}, "units": {"name": "units", "group": "Inputs", "definition": "random('in','cm')", "description": "", "templateType": "anything"}, "r_o": {"name": "r_o", "group": "Inputs", "definition": "qty(random(2..scalar(b)/2),units)", "description": "r
", "templateType": "anything"}, "debug": {"name": "debug", "group": "Inputs", "definition": "false", "description": "", "templateType": "anything"}, "Ix3": {"name": "Ix3", "group": "Ix", "definition": "Ibarx3 + A3 h h", "description": "", "templateType": "anything"}, "Iy1": {"name": "Iy1", "group": "Iy", "definition": "h b b b /3", "description": "", "templateType": "anything"}, "Ix": {"name": "Ix", "group": "Ix", "definition": "Ix1 + Ix2 - Ix3", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "r_i < h", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Inputs", "variables": ["b", "h", "r_o", "r_i", "units", "debug", "ggbArgs"]}, {"name": "Ix", "variables": ["Ix1", "Ibarx2", "Ix2", "d2", "Ibarx3", "Ix3", "Ix", "kx"]}, {"name": "Area", "variables": ["A1", "A2", "A3", "A"]}, {"name": "Iy", "variables": ["Iy1", "Ibary2", "Iy2", "Ibary3", "Iy3", "Iy", "ky"]}], "functions": {"display": {"parameters": [["q", "quantity"]], "type": "string", "language": "jme", "definition": "string(siground(q,4))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "For the x-axis", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$I_x$ = [[0]] $k_x$ = [[1]]
\n{display(Ix)} {display(kx)}
", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "I", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "Ix", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "k", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "kx", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "For the y axis", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$I_y$ = [[0]] $k_y$ = [[1]]
\n{display(Iy)} {display(ky)}
", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "I", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "Iy", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}, {"type": "engineering-answer", "useCustomName": true, "customName": "k", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "ky", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}