Moment of inertia of this body

In summary, the conversation discusses finding the moment of inertia of a rod and a sphere around a given axis. The problem statement only provides the length and mass of the rod, as well as the radius and mass of the sphere. The attempt at a solution involves using the parallel axis theorem to calculate the inertia at the given axis, and the conversation concludes with the realization that the professor had not previously mentioned this method.
  • #1
Mohamed Essam
24
0
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 ,
 

Attachments

  • IMG_0497.JPG
    IMG_0497.JPG
    21.6 KB · Views: 401
Last edited by a moderator:
Physics news on Phys.org
  • #2
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...
 
  • #3
IMG_0498.JPG
berkeman said:
Can you post a better image please? That one is way too dark to read...
 
  • #4
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.
 
  • #5
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 ) ??
 
  • #6
Mohamed Essam said:
by this equation ( Inertia at axis =Inertia at axis from centre of mass + mass*distance between the two axis^2 ) ??
Yes.
 
  • #7
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
 
  • #8
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?
 
  • #9
haruspex said:
That's quite an omission. All good now?
Yeah , thank you so much.
 

1. What is moment of inertia of a body?

The moment of inertia of a body is a measure of its resistance to rotational motion. It is a physical property that depends on the mass distribution of the body and the axis of rotation.

2. How is moment of inertia calculated?

Moment of inertia is calculated by integrating the mass of each element of the body with respect to the square of its distance from the axis of rotation. The formula is I = ∫r²dm, where I is the moment of inertia, r is the distance from the axis of rotation, and dm is the mass of the element.

3. What is the unit of moment of inertia?

The unit of moment of inertia depends on the system of units being used. In the SI system, the unit of moment of inertia is kg*m². In the US customary system, it is lb*ft².

4. How does the shape of a body affect its moment of inertia?

The moment of inertia is directly affected by the mass distribution of a body. The shape of a body plays a significant role in determining its mass distribution. For example, a body with most of its mass concentrated towards the axis of rotation will have a smaller moment of inertia compared to a body with the same mass spread out away from the axis.

5. What is the significance of moment of inertia in rotational motion?

The moment of inertia is an important parameter in rotational motion as it determines how much torque is needed to produce a given angular acceleration. It also affects the stability and energy storage of rotating objects. For example, objects with higher moment of inertia are more difficult to rotate and have more stability compared to objects with lower moment of inertia.

Similar threads

Correct Use of the Parallel Axis Theorem for Moment of Inertia
    • Introductory Physics Homework Help
Replies
2
Views
640
Moment of inertia of T bar about 3 axes
    • Introductory Physics Homework Help
Replies
21
Views
1K
Moment of inertia of a disk about an axis not passing through its CoM
    • Introductory Physics Homework Help
Replies
11
Views
1K
Question on Moment of Inertia Tensor of a Rotating Rigid Body
    • Introductory Physics Homework Help
Replies
4
Views
933
Collision between asteroids
    • Introductory Physics Homework Help
10
Replies
335
Views
8K
Calculate the moment of inertia of this body
    • Introductory Physics Homework Help
Replies
4
Views
962
Moment of inertia of a cuboid parallel to one of its faces (repost with diagram)
    • Introductory Physics Homework Help
Replies
25
Views
466
Parallel Axis Theorem Not Working
    • Introductory Physics Homework Help
Replies
28
Views
551
Calculating Moment of Inertia for Hollow Cylinder w/ Water
    • Introductory Physics Homework Help
2
Replies
40
Views
2K
Stability of rigid body rotation about different axes
    • Introductory Physics Homework Help
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top