How to Calculate the Moment of Inertia for a Rod and Sphere System?

AI Thread Summary
To calculate the moment of inertia for a rod and sphere system, the discussion emphasizes using standard formulas and the parallel axis theorem instead of integration. Participants clarify that the moment of inertia can be found by adding the inertia about the center of mass to the product of mass and the square of the distance between axes. The original poster struggled with the integration method and lacked knowledge of the parallel axis theorem, which was not covered in their coursework. After receiving guidance, they expressed gratitude for the clarification. The conversation highlights the importance of foundational concepts in physics for solving such problems effectively.
Mohamed Essam
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1. The problem statement, all variables and given/known
See attachment , it only gives me length of rod and it's mass and radius of sphere and its mass and the place of the axis

Homework Equations


I=mr^2

The Attempt at a Solution


I tried to get the moment of intertia of rod by integration from -L/4 to 3L/4 , but i cannot get the intertia of sphere around the axis ,
 

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Mohamed Essam said:
1. The problem statement, all variables and given/known
See attachment , it only gives me length of rod and it's mass and radius of sphere and its mass and the place of the axis

Homework Equations


I=mr^2

The Attempt at a Solution


I tried to get the moment of intertia of rod by integration from -L/4 to 3L/4 , but i cannot get the intertia of sphere around the axis ,
Can you post a better image please? That one is way too dark to read...
 
IMG_0498.JPG
berkeman said:
Can you post a better image please? That one is way too dark to read...
 
Mohamed Essam said:
I tried to get the moment of intertia of rod by integration from -L/4 to 3L/4 , but i cannot get the intertia of sphere around the axis
You should not need to do any integration. For such a question, I would expect to be allowed to quote standard formulas for moments about mass centres and apply the parallel axis theorem.
 
haruspex said:
You should not need to do any integration. For such a question, I would expect to be allowed to quote standard formulas for moments about mass centres and apply the parallel axis theorem.
by this equation ( Inertia at axis =Inertia at axis from centre of mass + mass*distance between the two axis^2 ) ??
 
Mohamed Essam said:
by this equation ( Inertia at axis =Inertia at axis from centre of mass + mass*distance between the two axis^2 ) ??
Yes.
 
haruspex said:
Yes.
Thank you for telling me the way of parallel axis theorem i wasn't know it , my physics professor in university didn't tell us anything about it and he puts it in an exam
 
Mohamed Essam said:
Thank you for telling me the way of parallel axis theorem i wasn't know it , my physics professor in university didn't tell us anything about it and he puts it in an exam
That's quite an omission. All good now?
 
haruspex said:
That's quite an omission. All good now?
Yeah , thank you so much.
 
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