- #1
AakashPandita
- 157
- 0
Everybody says that the distance ,between the two axis, used in the formula, is perpendicular. But in the proof it was a hypotenuse. It was not perpendicular.
Proof of parallel axis theorem.
- Thread starter AakashPandita
- Start date
In summary, the proof for the parallel axis theorem involves the use of two sets of axes - the original axes and the transformed axes, which are parallel to each other. The theorem covers displacement in both the x and y directions. The proof uses the formula I = Icom + Mh^2, where I is the moment of inertia, Icom is the moment of inertia about the center of mass, M is the mass, and h is the distance between the two axes. In the proof, the distance h is not perpendicular, but rather a hypotenuse. This is shown in the formula I = \int (x^2 + y^2) dm - 2a \int x dm - 2b \int y
- #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
- 12,811
- 1,671
Be specific about which proof. Provide details.
- #3
AakashPandita
- 157
- 0
- #4
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
- 12,811
- 1,671
The original axes and the transformed axes are parallel to one another. The theorem covers a displacement not only in the x direction, but the y direction as well. I don't see what your question is about.
- #5
What is the parallel axis theorem?
The parallel axis theorem is a principle in physics that states that the moment of inertia of a rigid body about any axis parallel to its center of mass is equal to the moment of inertia about an axis through its center of mass plus the product of the mass of the body and the square of the distance between the two axes.
Why is the parallel axis theorem important?
The parallel axis theorem is important because it allows us to calculate the moment of inertia of a rigid body about any arbitrary axis, rather than just the center of mass. This is useful in many applications, such as in engineering and physics, where the moment of inertia is an important parameter for understanding the motion of objects.
How is the parallel axis theorem derived?
The parallel axis theorem can be derived using the moment of inertia for a point mass and the parallel axis theorem for a system of particles. By integrating over the entire body, we can arrive at the general parallel axis theorem for a rigid body.
What are the assumptions of the parallel axis theorem?
The parallel axis theorem assumes that the body is rigid and has a constant mass distribution. It also assumes that the axis of rotation is parallel to the axis through the center of mass.
How is the parallel axis theorem applied in real-world scenarios?
The parallel axis theorem is applied in various real-world scenarios, such as in the design of rotating machinery, calculation of moments of inertia in engineering problems, and in understanding the motion of objects in space. It is also used in physics experiments to analyze the rotational motion of objects.
Similar threads
-
Classical Physics
-
Classical Physics
-
Introductory Physics Homework Help
-
Mechanics
-
Classical Physics
-
Classical Physics
-
Introductory Physics Homework Help
-
Calculus and Beyond Homework Help