• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Moment of inertia of this shape about the x-axis

  • Thread starter jisbon
  • Start date
257
23
Homework Statement
Calculate moment of inertia of a 2d plane rotating about x axis. Mass per unit area of plate = ##1.4g/cm^2## , total mass = 25.2g
Homework Equations
##I=\int y^2 dm##
1567752378952.png

I've attempted this question, but the answer seems to be incorrect. Here's my workings:
##I=\int y^2 dm## - standard equation
##dM = \mu * dy * x## - take small slice and find mass of it
##x = 4y-16## - convert equation in terms of x to sub in later
##dM = \mu * dy * 4y-16##
##I=\int y^2 \mu * dy * 4y-16##
##I=\mu\int y^2(4y-16) dy##
##I=\mu\int 4y^3-16y^2 dy##
##I=\mu \int_{0}^{3} 4y^3-16y^2 dy## = 12.6, which is not the answer.
Any clues why?
 

Delta2

Homework Helper
Insights Author
Gold Member
2,400
675
Something wrong in your final calculation of the integral, I found it to be
##\int_0^3 (4y^3-16y^2 )dy=-63## and if ##\mu=1.4## then the final value should be -88.2. The minus sign can be explained (because you took ##x=4y-16## while i believe it is ##x=16-4y##).
 
257
23
Something wrong in your final calculation of the integral, I found it to be
##\int_0^3 (4y^3-16y^2 )dy=-63## and if ##\mu=1.4## then the final value should be -88.2. The minus sign can be explained (because you took ##x=4y-16## while i believe it is ##x=16-4y##).
The answer seems to be 37.8g/cm^2 though :/ Any ideas on this?
 

Delta2

Homework Helper
Insights Author
Gold Member
2,400
675
At the moment I cant spot any other mistake. Are we sure that the equation of y(x) as well as the boundaries of integration (from y=0 to y=3 or from x=4 to x=16) are correct?
 
257
23
At the moment I cant spot any other mistake. Are we sure that the equation of y(x) as well as the boundaries of integration (from y=0 to y=3 or from x=4 to x=16) are correct?
Equation of y is y= -1/4x+4 , so it should be correct :/
 

Delta2

Homework Helper
Insights Author
Gold Member
2,400
675
I think I spotted a mistake, the mass element should be ##dM=\mu(x-4)dy## so the final integral should be ##\mu\int_0^3 (12y^2-4y^3)dy##
 
Last edited:

Want to reply to this thread?

"Moment of inertia of this shape about the x-axis" You must log in or register to reply here.

Related Threads for: Moment of inertia of this shape about the x-axis

Replies
5
Views
5K
Replies
4
Views
555
Replies
5
Views
3K
Replies
8
Views
6K
Replies
10
Views
3K
Replies
6
Views
593

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top