The moment of inertia, or rotational inertia, determines the torque needed for a desired angular acceleration about a rotational axis. Like inertial mass is the resistance to being linearly accelerated, the moment of inertial is the resistance to being rotationally accelerated.
Questions tagged [moment-of-inertia]
886 questions
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What is the physical significance of the off-diagonal moment of inertia matrix elements?
The tensor of moment of inertia contains six off-diagonal matrix elements, which vanish if we choose a reference frame aligned with the principal axes of the rotating rigid body; the angular momentum vector is then parallel to the angular velocity.…
noir1993
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What's the physical significance of the off-diagonal element in the matrix of moment of inertia
In classical mechanics about rotation of rigid object, the general problem is to study the rotation on a given axis so we need to figure out the moment of inertia around some axes. In 3-dimensional case, we have a matrix (i.e. moment of inertia…
user1285419
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Compute an object's inertia around an arbitrary axis, using its known values for the x, y and z axes
I need to input inertia data into a bio-mechanical simulation program. I can find inertia data for parts of the human body, around the normal axes.
I know the parallel axis theorem, so I can compute the inertia for the body parts in different…
cvr
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Moment of inertia of a rod, what is wrong?
The moment of inertia (MOI) of a rod that rotates around its center is $\frac{1}{12} m l^2$, while a rod that rotates around its end is $\frac{1}{3} ml^2$, as listed here.
That doesn't sound right - please see the image. A rod that rotates around…
user2174870
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Why isn't the moment of inertia of a cylindrical tube the difference of those of two cylinders?
The moment of inertia of a solid cylinder is $\frac{1}{2}mr^2$, and the moment of inertia of a composite object is the sum of the moments of inertia of the objects it consists of minus the moment of inertia of any air space. That would imply that…
iTechnical
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Interpretation of Moment of Inertia Tensor
Is there a simple physical interpretation for the off-diagonal entries of the moment of inertia tensor?
I know that those entries are de facto necessary to use the tensor to calculate quanties like angular momentum or rotational kinetic energy, and…
Chill2Macht
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Why is second moment of area often referred as moment of inertia?
In many references, mostly civil engineering, the second moment of area is referred as Moment of Inertia. Is that "really" correct? From my understanding, moment of inertia is analogous to mass in rotational motion, not the second moment of area.
ukg
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What is physical significance of product of Inertia?
I have read in available sources that product of inertia is just a term that is defined because it is useful in calculating the minimum and maximum moments of inertia of a body and also in finding the moments of inertia about a rotated system of…
user87745
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Calculation of Moment of inertia by exploiting the fact that it only depends upon the distribution of mass with respect to the principal axis
First of all what do I even mean when I say ‘the method of exploitation of the fact that only mass distribution is what matters with respect to the principal axis(I will be referring this method as exploitation method for the post)’. let me…
Rishi
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Is moment of inertia additive? If so, why doesn't adding two halves of solid box work?
I'm doing a project where I want to calculate the moment of inertia for some objects. I've broken the objects down into simple objects like cubes, spheres, cylinders, etc -- things I know the moment of inertia tensor for. My plan was to take these…
Stan Shunpike
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Doubt on the derivation of moment of inertia
I saw the derivation of moment of inertia for a rigid body through an axis of rotation. The derivation did integration of $r^2dm$, which I understood. But my doubt is why can I do the derivation in this way?
First we will find the centre of mass of…
Krishna behera
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Is there any physical example or application of Product Moment of inertia?
I think similar questions have already been asked but they are just similar not same.
I completely agree with the fact that product moment of inertia is a physical quantity but i am not able to find a satisfactory(as per me) example which tells the…
Manish
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How to find the moment of inertia for a cylindrical segment
I want to find the moment of inertia for a cylindrical segment, show below:
On Wolfram MathWorld, I found a formula for the volume of a cylindrical segment. Let
$$h(r,\theta) = h_1 +\frac{1}{2}\left(1+\frac{r}{R}\cos(\theta) \right)…
Stan Shunpike
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Does the moment of inertia scale quintically for similar solids?
In this list
https://en.wikipedia.org/wiki/List_of_moments_of_inertia
there appears to be the pattern that the moment of inertia of a similar solid scales quintically. For example, given a sphere of radius $r_1$ with mass $m_1$, we have
$$I_1 =…
ignoramus
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Can someone give me an intuitive meaning of the term "moment of area".?
Moment if inertia is the rotational analogue of mass. But I can't get the idea of the term "moment of area". What does it mean?
user137871
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