Join TSR now and get all your revision questions answeredSign up now

M5 June 2010 Q3a Watch

    • Thread Starter
    Offline

    0
    ReputationRep:
    3. A uniform lamina ABC of mass m is in the shape of an isosceles triangle with
    AB = AC = 5a and BC = 8a. (a) Show, using integration, that the moment of inertia of the lamina about an axisthrough A, parallel to BC, is 92 ma2 .
    The answer should read (9/2)ma^2. In the mark scheme for this question it makes no reference to the use of the standard result for a uniform rod of length 2l, and neither does the question, and yet surely this is essential since you need the summation of all the strip's moment of inertia to get the total moment of inertia.

    Thank you in advance!!!!
    Offline

    3
    ReputationRep:
    (Original post by mathsmusician)
    3. A uniform lamina ABC of mass m is in the shape of an isosceles triangle with
    AB = AC = 5a and BC = 8a. (a) Show, using integration, that the moment of inertia of the lamina about an axisthrough A, parallel to BC, is 92 ma2 .
    The answer should read (9/2)ma^2. In the mark scheme for this question it makes no reference to the use of the standard result for a uniform rod of length 2l, and neither does the question, and yet surely this is essential since you need the summation of all the strip's moment of inertia to get the total moment of inertia.

    Thank you in advance!!!!
    The "standard result" for the M of I of a rod is about an axis perpendicular to the rod. That is not needed in this question (or at least, the way the mark scheme and I have done it). The lamina is split into strips which are parallel to BC. All of the typical strip is a distance x from A, so its M of I about an axis through A , parallel to BC is mass of strip times x^2.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Okay thanks that makes sense. What I am wondering now is why can't this method always be applied....why in some cases do you have to use the standard result for the M.I. of a rod to work out the M.I. of the lamina. For example in June 2013 Q5 there's an almost identical problem, the only difference is that the axis of rotation is perpendicular to the base of the triangle, not parallel to it as in this question. For this type of question, couldn't you simply use the same method without using a standard result, and use the perpendicular rule to get the final answer?
    Offline

    3
    ReputationRep:
    (Original post by mathsmusician)
    Okay thanks that makes sense. What I am wondering now is why can't this method always be applied....why in some cases do you have to use the standard result for the M.I. of a rod to work out the M.I. of the lamina. For example in June 2013 Q5 there's an almost identical problem, the only difference is that the axis of rotation is perpendicular to the base of the triangle, not parallel to it as in this question. For this type of question, couldn't you simply use the same method without using a standard result, and use the perpendicular rule to get the final answer?
    When you use perpendicular axes for a circle, for instance, you use the symmetry of the circle. You haven't got that symmetry for the triangle, as I see it.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Yep that answers my question. Thanks
 
 
 
Poll
What is your favourite film genre?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.