Moment of Inertia: Object w/ Rod & Sphere

In summary, the conversation discusses the moment of inertia for an object formed by attaching a uniform rod and sphere. The equations for calculating the moment of inertia are provided, with a mistake initially made in the second term due to not squaring the distance. The correct moment of inertia for the system is calculated to be 286.177 kg-m^2.
  • #1
cp255
54
0

Homework Statement



An object is formed by attaching a uniform, thin rod with a mass of mr = 6.91 kg and length L = 4.88 m to a uniform sphere with mass ms = 34.55 kg and radius R = 1.22 m. Note ms = 5mr and L = 4R.

What is the moment of inertia of the object about an axis at the left end of the rod?

attachment.php?attachmentid=56284&stc=1&d=1362266421.png


Homework Equations


I came up with these equations...
I_rod = (1/3) * mr * L^2
I_sphere = (2/5) * ms * R^2 + ms * (L + R)

The Attempt at a Solution



I think that the moment of inertia for the system is equal to the sum of I_rod and I_sphere. So I simply plugged in the relevant variables and got the answer of 286.177 kg-m^2 which is wrong. Are the equations above correct?
 

Attachments

  • momentofinertia1new.png
    momentofinertia1new.png
    947 bytes · Views: 3,025
Physics news on Phys.org
  • #2
cp255 said:
I_sphere = (2/5) * ms * R^2 + ms * (L + R)
That second term, from the parallel axis theorem, should have the distance squared.
 
  • #3
Thanks. That was stupid of me. I did the problem twice and made the same mistake twice.
 

Related to Moment of Inertia: Object w/ Rod & Sphere

1. What is the moment of inertia of an object with a rod and sphere?

The moment of inertia of an object with a rod and sphere depends on the mass and distribution of the mass of the object. It is a measure of an object's resistance to rotational motion.

2. How is the moment of inertia calculated for an object with a rod and sphere?

The moment of inertia for an object with a rod and sphere can be calculated by breaking the object into smaller parts, calculating the moment of inertia for each part, and then summing them together using the parallel axis theorem. Alternatively, it can be calculated using the formula I = mr², where I is the moment of inertia, m is the mass of the object, and r is the distance from the axis of rotation to the mass.

3. How does the distribution of mass affect the moment of inertia for an object with a rod and sphere?

The moment of inertia is directly affected by the distribution of mass. Objects with more mass located farther from the axis of rotation will have a higher moment of inertia, meaning they will be more resistant to rotational motion. Objects with mass concentrated closer to the axis of rotation will have a lower moment of inertia.

4. Can the moment of inertia of an object with a rod and sphere be changed?

Yes, the moment of inertia of an object with a rod and sphere can be changed by altering the distribution of mass. For example, if the mass is moved farther from the axis of rotation, the moment of inertia will increase.

5. How is the moment of inertia useful in physics?

The moment of inertia is an important concept in physics as it helps to explain rotational motion and the effects of mass distribution on an object. It is used in various calculations, such as calculating the torque needed to rotate an object or the angular acceleration of an object. It is also used in engineering and design to determine the stability and strength of structures.

Similar threads

Correct Use of the Parallel Axis Theorem for Moment of Inertia
    • Introductory Physics Homework Help
Replies
2
Views
713
Parallel Axis Theorem Not Working
    • Introductory Physics Homework Help
Replies
28
Views
605
Moment of inertia of T bar about 3 axes
    • Introductory Physics Homework Help
Replies
21
Views
1K
Two objects joined by a rectilinear cable rotating
    • Introductory Physics Homework Help
Replies
8
Views
149
Moment of inertia of a disk about an axis not passing through its CoM
    • Introductory Physics Homework Help
Replies
11
Views
2K
Moment of inertia of a disc using rods as differential elements
    • Introductory Physics Homework Help
Replies
8
Views
1K
Determine the moment of inertia of a bar and disk assembly
    • Introductory Physics Homework Help
Replies
3
Views
2K
Moment of inertia of a rod bent into a square
    • Introductory Physics Homework Help
Replies
12
Views
1K
Calculating Moment of Inertia for Hollow Cylinder w/ Water
    • Introductory Physics Homework Help
2
Replies
40
Views
3K
Moment of Inertia of this combined system?
    • Introductory Physics Homework Help
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top