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1answer
20 views

The dot product integral in the proof of the Parallel axis theorem

The first picture is a question about proving the Parallel axis theorem and the second is the solution. I have no problem with the solution except for the part which says that $$ \int 2\vec h ...
2
votes
1answer
18 views

Diagonal of a thin rectangular foil, inertial principal axis?

I'd like to know if the diagonal of a thin foil is an inertial principal axis. I know that if an axis isn't a symmetry axis then it isn't a principal axis. In the rectangle the diagonal isn't a ...
2
votes
2answers
67 views

Two particles have the same linear momentum but their angular momentum differ. Which's harder to stop?

Which one is harder to stop, a 2 kg particle moving in a circular path of radius 5 m , with angular velocity of 10 rad/s or a 2 kg particle moving in a circular path of radius 2 m with a angular ...
1
vote
1answer
36 views

How do I calculate the moment of inertia with velocity? [closed]

How do I calculate a total moment of inertia when I have point mass with velocity? It looks like this: If I understand correctly, firstly I have to find a center of mass. What do I do next?
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2answers
42 views

Moment of inertia of a body

I found the relation,$I=2\cdot T_\text{rot}$, where $I$ is the moment of inertia and $T_\text{rot}$ is the kinetic energy of rotation. Does moment of inertia depend on angular velocity? If it depends, ...
0
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1answer
33 views

How to calculate the moment of inertia of a 2 point mass system

I have 2 point masses $m_1$ and $m_2$ connected via a massless rigid rod to a center. $m_1$ is at the distance $r_1$ from the center and $m_2$ is at the distance $r_2$ from the center. How would i ...
1
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0answers
25 views

Parallel axis theorem non-uniform density [closed]

The parallel axis theorem says that if the moment of inertia of a body rotating about the body's centre of mass is $I_{cm}$, then the moment of inertia of the body rotating about an axis parallel to ...
3
votes
1answer
50 views

Moment of inertia meaning?

Why is the formula for calculating the moment of inertia this integral $$ \int r^2 dm~? $$ I understand the way we derived this formula from looking at the distribution of kinetic energy of a ...
0
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1answer
47 views

How do momentum get transferred?

Simple Question , Consider two objects namely $A$ and $B$ where $B$ is stationary and $A$ is moving towards $B$ with velocity $v$. When the two objects touch each other what does actually happen ...
1
vote
4answers
47 views

moment of inertia when a shape is cut [closed]

A disk of radius $r_1$ is cut from a disk of radius $r_2$, $(r_2>r_1)$ from the middle of the bigger disk . If the annular ring left has mass $M$ then find the moment of inertia about the axis ...
0
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1answer
18 views

If $z_G$ is a principal axis that goes through the center of mass, are every other axes $z$ parralel to $z_G$ also principal axes?

I know that : If $y$ is a principal axis $\iff$ you can express the angular momentum with respect to a point $Y$ on that axis (if the solid is rotating around that axis of course) with the formula : ...
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votes
2answers
26 views

Calculating moment of inertia if a solid Sphere, using infinitesimally small spheres

Consider a Sphere of mass M, and volume V = (4/3)π(r)^3 and uniform density p, If I want to get its moment of inertia around an axis running through its centroid then I shall Integrate (dm r^2) And ...
0
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1answer
48 views

Moment of inertia of orbiting sphere

Is the moment of inertia of a sphere orbiting some object equal to the moment of inertia of a point mass at the same distance away from the object?
2
votes
2answers
72 views

Calculating moment of inertia for a cylinder?

I'm trying to calculate the moment of inertia for a cylinder about a longitudinal axis, but I don't know where I went wrong with my approach. $$I=\int r^2 dm$$ Assuming constant density: ...
3
votes
1answer
55 views

Parallel axis theorem: adding mass

I'm going through a worked physics problem and have a question about the parallel axis theorem regarding only adding mass while not changing is axis of rotation. Here is the problem: A physics ...
1
vote
1answer
68 views

Is moment of inertia numerically additive?

NOTE: The following argument is being made for square only, not any general shape. We have this square plate: From Perpendicular Axis theorem, $$I_1 + I_2 = I_z \\ I_3 + I_4 = I_z$$ Also, ...
3
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4answers
127 views

Can a die be made unfair without changing the center of mass or the exterior?

This question came from trying to design some 3d printed dnd dice. I think it's possible to make a die unfair without changing the center of mass or affecting the exterior shape*, but I'm not sure ...
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2answers
105 views

Moment of inertia of solid cube about body diagonal

How do I find the above mentioned moment of inertia? Steps I've tried: 1.) Triple integrations that proved to be to big. 2.) I noticed that the if we split a $2\times 2\times 2$ into individual ...
0
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1answer
84 views

Rotation of fluid filled cylinders [closed]

Given two cylinders of same mass , one completely made out of solid metal and the other a hollow one which has been filled with a viscous fluid say oil. Both have the same mass.Now if they are placed ...
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1answer
40 views

Second moment of area in parallel axis theorem

In parallel axis theorem why Ig second moment of area on axis passing through centre of gravity, is not zero. Even distance between axis and centre of gravity is zero.
0
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2answers
30 views

Is it okay to use the same moment of inertia formula for both a door turning on hinge and a long thin rod rotating at its end?

My book says you can redistribute the mass elements of a object to simplify its moment of inertia formula. But squeezing a door into a rod would change its density. Does it matter?
0
votes
1answer
28 views

What are some characteristics of r as in $\tau = mr^2\alpha$?

Can r just be the distance from an object center of mass to the axis of rotation? If not, it will be very hard to calculate r for things that are not particles, which doesn't exist in real life. ...
0
votes
1answer
21 views

Using moment of intertia to shortest travel time

Consider a ball and a cylinder with mass $m$, half diameter $r$ and a moment of inertia, around the axis of rotation $I$. Define $I^*=\frac{I}{mr^2}$. Determine $I^*$ for a hollow ball and a ...
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0answers
30 views

Doubt in a question about a body rolling up a ramp [closed]

I encountered a question in this year's paper of an exam, and I am in confusion. The question says: A body with mass $m$ and radius $R$ and rolling without slipping with speed $V$, moves up a ...
0
votes
1answer
63 views

Why do we need theorems like **Parallel Axis Theorem**

In rigid body pure rotation, quantities like $\omega, \tau, L, I, r_i$ (symbol with usual meaning) are axis dependent. Assume rigid body to be sphere rotating about the axis passing trough the center. ...
0
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1answer
87 views

Moments of Inertia (Calculus Application)

Hi so here's the problem I'm working on: Consider a 2 meter-long rod with linear mass density $\lambda(x)=x$ kg/m, where $x=0$ corresponds to one end of the rod. (a) Determine the centre of ...
0
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1answer
39 views

How can I determine the vector parallel to the long molecular axis?

I have a molecule in a system (the molecule is not in the center) with determined coordinates of all atoms. One of my molecule is on the picture below What I need is to determine the vector that ...
0
votes
1answer
60 views

Moment of Inertia of 'U' shaped rod hanging from celling [closed]

The ends of three identical uniform thin rods are joined at right angles to form a U-shaped body. A freely rotating axle $A$ is attached to one end of this body. The axle is then fixed to the ceiling ...
0
votes
0answers
40 views

What is required for a time-varying moment of inertia matrix?

Let me preface this question by stating that I am familiar with euler's equations for rigid body dynamics, torque and angular momentum. Despite the math, I'm still a little fuzzy about certain ...
0
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0answers
39 views

Hemisphere moment of inertia with varying density

Find the moment of inertia through axis of symmetry of a hemisphere given by $x^2+y^2+z^2 \leq R^2$ and $0 \leq z$ with density $\rho = \alpha \sqrt{x^2+y^2+z^2}$ Since the density is radius ...
0
votes
0answers
25 views

How rotational force calculation depends on the distance between the point of force application and the axis of rotation?

I don't understand how the perpendicular distance between the point of force and the axis of rotation gets involved in the calculation of the rotational effect of that force.Is it about rotational ...
-1
votes
1answer
171 views

Moment of inertia of disk with off center hole [closed]

So I am given the figure shown below and told to find the moment of inertia if we have that the mass of the shaded region is $M$. I think I have to find the total mass without the hole and the mass ...
2
votes
1answer
65 views

Moment of Inertia (Feynman)

Two balls of equal radius and mass, free to roll on a horizontal plane, are separated by a distance $L$ large compared to their radius. One ball is solid, the other hollow, and they are attracted by a ...
-1
votes
1answer
61 views

How do I properly apply the parallel axis theorem to a rod-sphere system rotating about its center of mass?

In the image below you see a rod with a sphere attached to its right side. The rod-sphere system is rotating around the entire system's center of mass. How do I apply parallel axis theorem to find the ...
0
votes
1answer
8 views

Calculating the force $F$ for wich $S_2$ will be in uniform motion

The sketch is given: The double pulley groove of radius $r=5\;\mathrm{cm}$ and $R=10\;\mathrm{cm}$ is in rotation Two inextensible wires of negligible masses are wound around ...
0
votes
1answer
82 views

What does the $a$ stand for in this picture? (And some clarification)

$$ I_{triangle} = \frac{b^3h-b^2ha+bha^2+bh^3}{36} $$ $$ I_{total} = \sum^n_{k=1}(I_{triangle}+Md^2)_k $$ Source is here. I'm trying to understand the mass moment of inertia in order to create a ...
1
vote
1answer
48 views

3D Dynamics: determining the moments of inertia on a plate with a couple

My Mechanical textbook (Bedford & Fowler 4th Edition) has a worked out example for determining a couple using euler's equations. This is not a homework question (at least I don't think it is?), ...
0
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3answers
57 views

Is Conservation of Energy maintained when the orbit of a rotating mass increases in diameter?

I read an example where someone was explaining how the law of conservation of energy does not have to be maintained within a rotating mass even though angular momentum is maintained. The given ...
-1
votes
1answer
38 views

What is wrong with my moment of inertia calculation? [closed]

I've been stuck on what should be a straight-forward calculation which is making me question whether I actually understand multi-variable calculus. In particular, I always seem to get the wrong ...
1
vote
3answers
71 views

Why can't we use centre of mass to find moment of inertia?

While calculating moment of inertia for two point particles, we use $$ I = m_1r_1^2 + m_2r_2^2$$ While calculating moment of inertia of a plank(with mass $m$) around an axis halfway through its ...
3
votes
0answers
77 views

Where this relation for general non rigid motion comes from?

In Goldstein's Classical Mechanics book in the chapter about the dynamics of rigid bodies the equation $$\dfrac{dL_i}{dt}+\epsilon_{ijk}\omega_jL_k = N_i$$ is presented. Now, in one exercise, we are ...
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votes
1answer
53 views

Graphing $E_p = E_k + E_{rot}$

I am measuring the moment of inertia of a flywheel and using conservation of energy to work out the value (I am ignoring friction). So for the experiment I have to roll the flywheel down a slope (I ...
0
votes
3answers
213 views

Acceleration of body rolling down inclined plane

Acceleration of a body rolling down an inclined plane is given by: $$\frac{g\sin\theta}{1+\frac{k^2}{r^2}}$$ $g$=acceleration due to gravity $\theta$=angle of inclined plane $k$=radius of gyration ...
0
votes
1answer
88 views

Measuring the moment of inertia of a flywheel using simple pendulum motion

I've seen a method for experimentally determining the moment of inertia of a flywheel and I'm not sure whats the reasoning behind it. You attach a small weight $m_1$ to the flywheel's edge, it's ...
1
vote
1answer
34 views

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 ...
0
votes
2answers
84 views

How do you choose direction of moment of inertia?

If a car is accelerating forward from rest with no air resistance while weight and normal forces act on the wheels, in which direction is the moment of inertia? Is it positive, clockwise or anti ...
4
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2answers
114 views

Physical intuition about the inertia tensor

I'm studying Mechanics on Goldstein's book (Classical Mechanics) and Spivak's book (Physics for Mathematicians) and I'm in doubt about the physical intuition about the inertia tensor. On both books, ...
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0answers
25 views

Need reference on the minimum moment of inertia [duplicate]

I would like to know if there is a book on classical mechanics about the following Moment Of Inertia About Centre of Mass
0
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3answers
353 views

Moment of Inertia of an L-shaped object

A uniform thin bar formed into a L-shaped object of mass $m=2.5kg$ with a longer side of length $l=0.8m$ and a shorter side of length $l/2$. Initially the object is positioned with one end at the ...
2
votes
2answers
146 views

Which moment of intertia do I need to calculate torque

I'm trying to calculate the torque needed to rotate an array of solar panels. I've found some formulas for calculating torque, but they require moment of inertia. I designed this array in Autodesk ...