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2
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1answer
37 views

Why are the principal axes about the center of mass of a cube perpendicular to its faces?

I have calculated the moment of inertia tensor of a cube about its center of mass: $I=\dfrac{1}{6}Mb^2\{1\}$ where $\{1\}$ is the identity matrix. So the principal moments of inertia are all 1 (1 is ...
2
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2answers
53 views

Determine reaction forces on square frame

The square frame consists of four identical homogeneous rods of mass $m$. It lies in the vertical plane and can move in it due to the wheels situated in A and B. These wheels can slide ...
1
vote
1answer
35 views

Moment of inerta of square frame

A rod of length $l$ and mass $m$ has $ml^2/12$ as moment of inertia about an axis through its center of mass. Say now we take four identical copies of the rod above and form a square frame, whose ...
1
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1answer
42 views

Can moment of inertia be defined as function of mass?

For continuous bodies, moment of inertia is found as $$ \int dI = \int_{m_i}^{m_f} r^2(m) .dm$$ . Now, $$\int dx = \int_{u_i}^{u_f} f(u).du \implies X_f(u) = \int_{u_i} ^{u_f} f(u) .du + X_i(u)$$ , ...
1
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2answers
27 views

Does a bungee cord have a moment of inertia?

Does a bungee cord have a moment of inertia? I'm trying to understand to what extent a body must be rigid in order for the moment of inertia to be defined for that body. Since the distance between ...
0
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1answer
18 views

Period of swinging incomplete hula-hoop

I was working on a problem where I had to calculate the period of a swinging incomplete hula-hoop given its center of mass and radius. It only swings with very small amplitude so I considered the ...
1
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2answers
43 views

Flipping a bottle

I tried to do this experiment recently at school and my house. I started the experiment by having three same type of bottles with the labels A,B and C. Bottle A has been fully filled with water, ...
0
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1answer
28 views

Finding the moment of inertia of a lever [duplicate]

I am required to find the moment of inertia of the lever for a project in physics. This is my attempt: Please note that we have not been taught this yet in class so i have not been taught this ...
2
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3answers
127 views

Why is moment of inertia dependent on $r^2$ and not on $r$ ? (physical reason)

Moment of inertia is the mass equivalent in rotational dynamics. I know , by mathematical arguments, moment of inertia of a particle is $$ I = \text{mass} \cdot r^2$$ . But what is the physical ...
3
votes
2answers
147 views

Can moment of inertia be negative? [closed]

Q: Find out the moment of inertia of a uniform circular disc of radius $r$ & mass $M$ & the axis passes through a point on the circumference. My attempt: Let the axis passes through $O$ on ...
0
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0answers
40 views

Combining Moment of Inertia Tensors

In a physics simulation of rigid bodies, if I have a cube with a known mass and moment of inertia tensor, and I attach it to another cube with a known mass and moment of inertia tensor such that its ...
1
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0answers
40 views

Calculating rotation using moment of inertia [closed]

I have an object A. I know its theoretical moment of inertia. I have a string wrapped around object A. I then apply a certain tension to that string, causing the object A to spin for a certain ...
0
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0answers
52 views

Principal axes: Are they unique?

Mathematically, principal axes are the eigenvectors of the Inertia Tensor. Physically, They are the axes that satisfy , Angular momentum || Angular Velocity || Principal Axis. Inertia tensor depends ...
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0answers
62 views

Calculating the moment of inertia in bifilar pendulums

I'm an A2 student, and I've been looking into how experimental and theoretical determined mass moments of inertia differ. I came across a method (search Youtube for Measuring Mass Moment of Inertia - ...
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vote
3answers
106 views

Help with Conservation of Angular Momentum Question

An ice skater executes a spin about a vertical axis with her feet on a frictionless ice surface. In each hand she holds a small 5kg mass of which are both 1m from the rotation axis and the angular ...
1
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1answer
85 views

Can the angular momentum of any rigid body (symmetrical or asymmetrical) be found this way?

Can the angular momentum of anybody regardless of whether its symmetrical about the center of mass or not be found by finding the angular momentum about its center of mass and summing it up with the ...
1
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0answers
42 views

Area moment motivation

I have some intuition about the (second) moment of inertia, and there is some motivation to define this concept if we think about the $KE$ of a rotating body or the torque $\tau$ applied, for example, ...
0
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0answers
38 views

How to drive quadrotor moments of inertia

I would like to know how moments of inertia (i.e. around x,y and z axes) of a quadrotor is driven given the total mass and the distance from the origin of the quadrotor to the center of a $i$th ...
1
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2answers
104 views

Is a double integral required to find the moment of Inertia of a non-uniform sphere?

Consider some ball of given radius $R$, with a mass density function that depends on the radial variable, $\rho=\rho(r)$ where $r$ is the distance from the center of the sphere. What is the moment ...
0
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1answer
43 views

Determining flexural modulus by performing 3 point bending test using hollow cylindrical tube

I would like to decide the flexural modulus of the material of plastic tube by performing 3 point bending test according to the ASTM D 790 procedure. In ASTM D 790, the form of the specimen is ...
1
vote
1answer
61 views

Moment of inertia help [closed]

Okay so lets say I have a lever with 2 objects on it, object one and object 2. Object 1 has a mass of $m_1$ and is $r_1$ away from the fulcrum; object 2 has a mass of $m_2$ and is $r_2$ away from the ...
2
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2answers
128 views

Rolling of a disk and sphere

I am confused regarding the fact that when a disk is rolling on an inclined plane without slipping and similarly a solid sphere is rolling on an inclined plane without slipping then the sphere has ...
4
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2answers
266 views

Relation between torque and moment of inertia

I have seen 2 formulas: $\tau = I \alpha$ and $\tau = I \dot\omega + \omega \times I \omega$. Which one shall I use in which case please? Also, am I right to think that $\alpha$ from the first formula ...
1
vote
3answers
230 views

Moment of inertia of rods

Ok so I'm extremely comfortable with calculating moment of inertia of continuous bodies but how do we do it for a system not continuous. For example if 3 rods of mass $m$ and length $l$ are joined ...
1
vote
1answer
117 views

Moment of inertia from torque and angular acceleration measurements

I tried to calculate the moment of inertia of a quadcopter along its roll axis using two different methods and the results do not match. Method 1: measuring the period of a bifilar pendulum, I obtain ...
1
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0answers
44 views

Moment of Inertia of Polygons in the Plane [closed]

I was reading this link, which describes a method of finding the moment of inertia of a general convex polygon by splitting it into triangles. I then realized I have no idea on how to derive a such a ...
0
votes
1answer
38 views

How do I find the moment of inertia of a regular $n$-gon? [closed]

Of a regular $n$-gon with radius $R$ and mass $M$. Any hint to solving would also be acceptable. The result I'm looking for is $$I_{CM} = (1/2) MR^2 (1 - (2/3) \sin^2(\pi/n)).$$
1
vote
0answers
50 views

What is physical significance of product of Inertia? [duplicate]

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 ...
0
votes
1answer
47 views

Is the Moment of Intertia of A Thin Rod equal to The Moment of Intertia of a thin Strip?

This is the Moment of Intertia of a Thin rod I am not aware of a formula for a thin strip (or if there is any such formula). I was imagining a thin rod does not have a radius in the formula (thin ...
0
votes
1answer
87 views

Feynman's explanation of parallel axis theorem

In the book Feynman's Lectures on physics volume 1 chapter 19, He explains prallel axis theorem as follows. Suppose we have an object, and we want to find its moment of inertia around some ...
1
vote
1answer
58 views

Moment of inertia as a tensor

A professor at my university briefly stated that moment of inertia is a tensor and can be represented by a $3×3$ matrix. I don't have a good idea of what a tensor is, so I would be grateful if someone ...
0
votes
1answer
693 views

Practical usage of Moment of inertia

A small confusion in understanding the practical application of moment of interia . Why is most of the mass of the wheel concentrated on the rim ? I know that it is to increase the moment of inertia ...
0
votes
1answer
88 views

How much energy is necessary to set a year to exactly 360 days

How much energy would be necessary to slow down Earth rotation such that a year was 360 days long? In the same spirit: how much energy would be necessary to make the Earth rotate faster around the ...
1
vote
1answer
114 views

Water bottle moment of inertia

I've noticed that I can make a full water bottle spin about its short axis easier than I can make it spin when it is 1/4 or 1/2 full. Also, when it is spun and is not full, the geometric center of the ...
1
vote
1answer
90 views

Would days be longer as the polar ice caps melt? [duplicate]

I got question in my mind striking for several days but not able to prove it, suppose polar ice on earth melt, would the days be longer? My friend said it was due to moment of inertia of the earth ...
-2
votes
1answer
135 views

What formula connects the moment of inertia and angular velocity? [duplicate]

I need to determine angular velocity of a disc when a man with given mass and speed whacks on the edge of it. I calculated the total moment of inertia of disc and body, how do I calculate the ...
2
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0answers
35 views

Fractional-Order Moments

Commonly seen in physics(and statistics) are the concepts of moments of order zero(mass), one(center of mass), and two(moment of inertia). In statistics a third moment (referred to as skewness) also ...
0
votes
1answer
43 views

At the instant of release of an object from rest. Is the only force that can act its weight?

Q3 from a mechanics exam past paper: I can do parts i) and ii) but for iii) in finding the angular acceleration, i used $C=I\alpha$, where $C$ is the applied couple or torque, $I$ is the moment of ...
0
votes
1answer
37 views

What does an $n$-body system with constant $T$ and $U$ look like?

Can someone give an example of a system where the kinetic $T$ and potential $U$ energy are constant (but not zero)? Here's what I have in mind: Say you have $n-1$ satellites of negligible mass ...
0
votes
1answer
79 views

Centre of mass, integral

I was answering a question on proving the parallel axis thereom for angular momentum and came across this: $$\int Yy'dm=Y\int y' dm=0$$ Where the position of the center of mass of an object is given ...
0
votes
1answer
287 views

Moment of inertia of a cylinder about its base

I've tried to find the moment of inertia of a cylinder rotating about an axis parallel to its base (i.e about the 'End diameter') as one can see here . But when I checked my results with different ...
1
vote
2answers
95 views

Rotational inertia of a ball

This question refers to the solution of problem 12 here. It involves a spherical shell of mass $M$ filled with frictionless fluid of mass $M$ rolling down an inclined plane. (This is problem 12 of ...
2
votes
1answer
129 views

Why is the inertia ellipsoid of a higher symmetry than the rigid body?

I was always puzzled by this fact. A uniform cube has a sphere-shaped inertia ellipsoid. The sphere has a higher symmetry then the cube. Is there any deep reason or implication behind it?
1
vote
1answer
238 views

Inertia tensor of a spherical cap

I'm trying to calculate the inertia tensor of a spherical cap (a piece of a sphere) like the one shown below. The origin (not shown) is located at the center of the whole sphere and the axes ...
4
votes
2answers
201 views

Weighing head by angular momentum

A popular Phys.S.E question asks how can I measure the weight of my head. One of the answers suggests measuring the moment of inertia. My suggestion was to construct an apparatus that places the ...
1
vote
1answer
699 views

Principle Axes of inertia and moments of inertia

Principal axes of inertia is defined as the eigenvectors of the inertia tensor matrices. I understand that a diagonalised tensor can yield these axes, but why are they necessarily form the axes of a ...
-1
votes
1answer
72 views

How do two rigid bodies with different 3rd moment of inertia rotate differently?

If rigid bodies $R_1$ and $R_2$ has exactly same total mass $M$, central of mass, and rotational inertia $I$, but different third moment of inertia $M_3$, how would they move/rotate differently? ...
1
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2answers
42 views

Terminologies for moment of inertia

Perhaps someone can suggest the right terms for the following mathematical objects related to moment of inertia? A inertia tensor $I$. $$I \equiv \begin{bmatrix} I_{1,1} & I_{1,2} & I_{1,3} ...
1
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3answers
54 views

Moment of inertia of a cylinder [closed]

When I tried to calculate the moment of inertia ($I_C$) of a cylinder (mass M, height H, radius R) around the rotating axis going symmetrically through its middle, I came up with a different result ...
1
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0answers
48 views

Under what conditions are the products of inertia (off diagonal elements of inertia tensor) non-zero?

Under what conditions are the products of inertia (off-diagonal elements of inertia tensor) non-zero? It seems that for many objects, constructing the moment of inertia tensor results in something ...