What is the moment of inertia for a sphere rotating about a tangent axis?

In summary, the moment of inertia for a solid sphere rotating about an axis tangent to its surface is the same as the moment of inertia for a sphere with the axis through its center. The axis of rotation is touching the surface of the sphere at one point, which is the definition of tangent. The parallel axis theorem can be used to calculate the moment of inertia at a point other than the axis through the center, as long as the axis is parallel to the center axis. This information can be easily found in textbooks and online resources.
  • #1
danielatha4
113
0
Can someone please tell me the moment of inertia for a solid sphere rotating about an axis tangent to its surface?
 
Physics news on Phys.org
  • #2
What does tangent to its surface mean? Where is the axis of rotation?
 
  • #3
The axis of rotation is touching the surface of the sphere at one point. That is the definition of tangent. Can it be treated as a point particle distance R from the axis?
 
  • #4
Parallel axis theorem?
 
  • #5
Sorry, never heard of that. It's not the goal of the assignment to figure out the moment of inertia around the axis tangent to the surface, but it would be a useful tool.
 
  • #6
Well look it up, it is not that difficult. It allows you to use the moment of inertia of a sphere (axis through center) to calculate the moment of inertia somewhere else as long as the other axis is parallel to the axis through the center. And finding the moment of inertia with axis through center is in almost every textbook and on the internet. http://en.wikipedia.org/wiki/Parallel_axis_theorem
 

FAQ: What is the moment of inertia for a sphere rotating about a tangent axis?

What is the formula for calculating moment of inertia for a sphere?

The formula for moment of inertia for a solid sphere is I = (2/5) * M * R^2, where I is the moment of inertia, M is the mass of the sphere, and R is the radius of the sphere.

How does the moment of inertia change for a hollow sphere compared to a solid sphere?

The moment of inertia for a hollow sphere is I = (2/3) * M * R^2, which is greater than the moment of inertia for a solid sphere. This is because the mass is distributed farther from the axis of rotation in a hollow sphere, resulting in a larger moment of inertia.

3. What is the physical significance of moment of inertia for a sphere?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. For a sphere, the moment of inertia determines how difficult it is to start or stop its rotation, as well as how fast it will rotate for a given torque.

4. How is moment of inertia related to the mass and size of a sphere?

The moment of inertia for a sphere is directly proportional to its mass and the square of its radius. This means that as the mass or size of the sphere increases, the moment of inertia also increases.

5. Can the moment of inertia for a sphere be negative?

No, the moment of inertia for a sphere cannot be negative. It is always a positive value as it represents an object's resistance to changes in rotational motion.

Similar threads

Moment of Inertia of something that rotates
Replies
15
Views
1K
Understanding Kinetic Energy: Moment of Inertia and Rotational Motion
Replies
5
Views
1K
Moment of inertia of a double physical pendulum
Replies
4
Views
2K
What is the principal moment of inertia tensor for a lamina?
Replies
2
Views
2K
Moment of Inertia of an Ammonium Molecule
Replies
3
Views
3K
Correct Use of the Parallel Axis Theorem for Moment of Inertia
Replies
2
Views
1K
I Moment of Inertia about an axis and Torque about a point
Replies
5
Views
2K
I Resolve moment of inertia at an angle
Replies
2
Views
1K
Parallel Axis Theorem Not Working
Replies
28
Views
883
Moment of inertia of a disk about an axis not passing through its CoM
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top