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3answers
49 views

Why is moment of inertia for a point same as a ring

The moment of inertia of a point and ring are both $m R^2$. It is interesting that the formula for moment of inertia is exactly the same for both. Is there any physical reason why this is the case? I ...
-1
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0answers
11 views

How to calculate the inertia tensors of an irregular polygonal right prism?

I am attempting to program a physics simulation and need to do calculate the inertia tensors of a mesh constructed of a series of irregular polygonal prisms. Now, I am aware that you can calculate ...
1
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1answer
31 views

Symmetry axis and products of inertia

So if we have an object that has a symmetry axis let us say $z$-axis is a symmetry axis does this mean that the product of inertia $I_{zx} = I_{zy} = 0$? And if that is true why is it true ...
2
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1answer
49 views

Cylinder inside a cylinder - moment of inertia

A homogeneous cylinder with radius a and mass m rolls in a hollow cylinder with radius R. Determine the kinetic energy of the cylinder as function of $\dot{\theta}$. I'm sorry for ...
0
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0answers
18 views

Cylinder rotating inside another cylinder. [duplicate]

A homogeneous cylinder with radius a and mass m rolls in a hollow cylinder with radius R. Determine the kinetic energy of the cylinder as function of $\dot{\theta}$. I'm sorry for ...
0
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0answers
10 views

How is the inertia tensor (just diagonal elements) of a quarter disk related to the full disk one?

Let be a disk of radius $R$ and mass $M$ with an uniform distribution of mass $\sigma$, centered in the origin O, laying in the $OXY$ plane. If I know that $$I_x=I_y=\frac{1}{4}MR^2, \qquad ...
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0answers
16 views

Shaft acceleration with a gearbox

I'm trying to calculate the shaft acceleration when there is an engine, a gearbox, and a load. I've seen the equations which change the reflected inertia via the gear ratio, relate the speeds and ...
3
votes
1answer
108 views

Coin rolling, but not sliding. Kinetic energy

A homogeneous coin of mass M rolls, without sliding, along the x-axis with the axis of rotation being parallel to the z-axis. Let $\Theta$ be moment of inertia regarding that axis and $\vec{V}$ be ...
1
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1answer
65 views

Disc and hole - moment of inertia [closed]

Determine the moment of inertia of a homogeneous disc with density $\rho_0$ of radius R with a circular hole of radius R/2 and central radius R/2 regarding an axis perpendicular to the surface and ...
0
votes
1answer
63 views

Moment of Inertia of Water. [closed]

Determine the moment of inertia $\Theta$ of a water molecule ($m_H=m,m_O=M$) for a rotation around the axis which is perpendicular to the molecule plane and goes through the center of mass S of the ...
0
votes
1answer
39 views

Combining moments of Inertia in gear chain

I've got two objects connected by a rod along it's axis of rotation (e.g. a sphere on top of a flat cylinder rotating around it's symmetric axis). Assuming the effects of the rod are negligible, is ...
0
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1answer
40 views

Part/Object Geometry

Given Inertia Tensor, Principal axes vectors, Center of Gravity, and the Moments. Is it possible to obtain object/part dimensions?
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0answers
36 views

Alternative ways of calculating the principal moment of inertia

Let's say I am given 2x2 masses ($m$ and $m'$ have the same mass, just different coordinates): $m_1: (-a,b,0)$ $m_1':(a,-b,0)$ $m_2: (a,b,0)$ $m_2': (-a,-b,0)$ Due to symmetry the center of mass ...
0
votes
1answer
37 views

Moment of inertia tensor calculation [closed]

If I have a rigid body consists of three uniform rods, each of mass $m$ and length $2a$, held mutually perpendicular at their midpoints choose a coordinate system with the axes along the rod. So I ...
0
votes
2answers
78 views

Area Moment of Inertia about y axis of i Beam [closed]

I was wondering if anyone could give me some input on what I am doing wrong here, because it is driving me crazy. I am trying to calculate the area moment of inertia about the y axis of this I beam: ...
1
vote
1answer
89 views

Why does a diver changes his body positions before and after diving?

Before a diver dives in a pool, he changes his body positions several times. When he is about to jump from board he extends his arms and legs but sometime after jumping he closes his body in a ...
0
votes
1answer
62 views

Why do some approximations give exact results?

The moment of inertia of a sphere of mass $M$ and radius $R$ can be calculated exactly (meaning, with certainty) using integrals. The formula we get is $\frac{2}{3}MR^2$. However, there's an other ...
0
votes
1answer
47 views

Moment of inertia of a rod and ball system

I have a problem in which a rod of length $d$ has mass $m$ and a point mass of $2m$ is on the left end of it. I want to calculate the moments of inertia for several axes all perpendicular to the rod. ...
0
votes
1answer
63 views

Calculating the Moment of Inertia of a Ball (so close) [closed]

So I tried calculating the moment of inertia of a ball (or filled-in sphere) of radius $R$ and mass $M$, and got surprisingly close to the right answer using a simpler approach than I've seen used ...
1
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1answer
64 views

Moment of Inertia Calculation [closed]

A uniform disc has centre O, radius a and mass 2m. It is free to rotate in a vertical plane about a horizontal axis through O. A particle P of mass m is placed on the highest point of the rough edge ...
0
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0answers
42 views

Calculating the 3-dimensional torque on a non-uniform rigidbody given the angular acceleration about its center of mass

Say I have a rigidbody, made up of several point particles with known masses and positions relative to the center of mass. How would I find the torque on this rigidbody given its angular acceleration ...
1
vote
1answer
146 views

Approximating the moment of inertia of a quadcopter [closed]

I want to compute an approximated moment of inertia for my quadcopter: my idea is to take the frame and the electronics, approximate it as a sphere in the center of mass $M$ and radius $R$ (with ...
2
votes
0answers
32 views

What is the effect of vibrations on an object's properties?

What do vibrations do to an object's properties? By making an object vibrate at a high frequency (compared to its static state) would vibrations: Increase or reduce its moment of inertia? Increase ...
0
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0answers
30 views

A free axis of rotation

It is claimed that the free axes of rotation of a rigid body are the ones with the smallest and the largest moment of inertia. Why? How can we determine which free axis of rotation will be used?
0
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1answer
55 views

Cancelling internal forces/moments term when deriving inertial matrix

I am attempting to derive the inertial matrix for a general rigid body of mass $m$ as shown in the following diagram: The green vectors indicate the key position vectors: Position of centroid ...
0
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1answer
93 views

Moment of inertia of cylinder [closed]

How to calculate moment of inertia of a cylinder about an axis passing through its geometrical center and inclined at an angle (\theta) with vertical.
0
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1answer
124 views

How to derive (the dimensionless coefficient in front of) the moment of inertia for common shapes?

Is there a way to derive (the dimensionless coefficient in front of) the moment of inertia for common shapes? I assume it has to do with the density of the shape, but I'm having trouble seeing it. ...
0
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2answers
36 views

When I change the rpm of a turntable, how long does the turntable to get to the new rpm?

If the turntable was rotating at 16 rpm and I switched it to 30 rpm, is the change in speed pretty much instantaneous, or is their a period of acceleration? When I did it, the change appeared to be ...
1
vote
1answer
114 views

Torsion pendulum and determining the moment of inertia

(58. Polish Olympiad in Physics, final stage, 2009) We have a given element . We have to determine its moment of inertia. The idea is using a torsion pendulum. Some considerations lead us to a ...
2
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5answers
161 views

Moment Of Inertia About Centre of Mass

Why is moment of inertia minimum about centre of mass of any rigid body?
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1answer
91 views

If I bend a rod, will its moment of inertia change?

In the first picture, there is a homogeneous metal rod of length $2L$ and mass $M$. If it rotates around a normal axis passing by $O$ (which is the center of gravity), then its moment of inertia is: ...
0
votes
2answers
125 views

How to determinate the minimum period of oscillation for a physical pendulum? [closed]

A physical pendulum consists of a thin homogeneous rod of length $l$, suspended by a point $O$ at a distance $x$ from the center of gravity ($x<\frac{l}{2}$), oscillating in a vertical plane. ...
0
votes
1answer
97 views

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 ...
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4answers
2k views

Distinguishing between solid spheres and hollow spheres (equal mass)

If there are two spheres (hollow and solid) with equal mass and radius and we want to find the hollow sphere without using any equipment. What's the best way(s) to recognize the hollow sphere and ...
1
vote
1answer
151 views

Mass Moment of Inertia of combined objects

I have a small circular ring placed on a circular disc. The outer radius of the ring is same as the radius of the disc. I have worked out the difference of Moment of Inertia of the combined shape ...
1
vote
1answer
106 views

Moment of Inertia: uniform rigid rod on smooth plane [closed]

Consider a rod of length $b$ and mass $m$ on a smooth horizontal plane. A force is applied to one end of the rod. What is the acceleration $a$ and angular acceleration $\alpha$ of the other end of ...
1
vote
2answers
129 views

Moment of inertia for a triangle? [closed]

First, I fully admit this is one of the physics problems that we have as a homework. However, I am totally clueless how I am supposed to solve this. I do have an answer that I am supposed to get, but ...
1
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0answers
53 views

Rotational energy with moment of inertia tensor

Some objects have a single moment of inertia value while others like ellipsoids have a tensor, if I wanted to work out the rotational energy of an oblate spheroid rotating around its z axis could I ...
1
vote
2answers
64 views

Compute the inertial tensor and then solve the equation? [closed]

If the $J_{\Omega}$ is the following matrix, which is solved by ja72 in How to compute the inertia tensor ${\bf{J}} _{\Omega}$ of a body of revolution: $${\bf J} = \rho\, \begin{bmatrix} ...
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vote
1answer
125 views

Moment of inertia question

If we have five identical rigid rods, each of length l and mass m, are connected together to form the system shown in the figure. The system may rotate about an axis passing through AB. The question ...
1
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1answer
98 views

How to compute the inertia tensor ${\bf{J}} _{\Omega}$ of a body of revolution

Suppose that $\Omega$ is a body of revolution of the function $y=f(x), a\le x \le b$ around the $x$-axis, where $f(x)>0$ is continuous. How to compute the inertia tensor ${\bf{J}} _{\Omega}$? ...
0
votes
0answers
89 views

Second moment of area of a rod (not circular cross section)

I'm trying to calculate the stress induced in a rod by an end mass with an initial rate of rotation. My current idea to calculate this is: 1) Calculate the rotational stiffness of the rod 2) ...
0
votes
1answer
69 views

how to increase the moment of inertia of a hollow aluminium pipe without changing the outer diameter [closed]

how to increase the moment of inertia of a hollow aluminium pipe with external diameter fixed and only allowed to change the shape of internal section for example rectangular hole or extruded section ...
2
votes
1answer
113 views

Does the moment of inertia change?

I am currently working on a practice problem for my upcoming exam and I have difficulties getting my head around moment of inertia. If the ball has mass $m$ and is going around in a circle with ...
0
votes
1answer
106 views

Is the moment of inertia of the bicycle wheel relevant for keeping bicycle in the upright position? [duplicate]

When we were taught physics at school and the topic was the Inertia and Flywheel, they used as an example that the moment of inertia of the bicycle wheel is the reason why we are able to keep the ...
1
vote
3answers
126 views

How is this application of the parallel axis theorem wrong?

Let's say I have a rod of length $L$. The moment of inertia for spinning it around some point at a distance $d$ from one end can be calculated using the parallel axis theorem. Specifically, knowing ...
1
vote
2answers
105 views

Polar moment of inertia of a cylinder

So I know the polar moment of inertia of a solid cylinder is: $$ I= \frac{1}{2} mr^2 $$ My question arises with the polar moment of inertia uses for solid cylinders in my mechanics of materials book, ...
1
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1answer
245 views

Why to use radius of gyration? [closed]

I know the definition of radius of gyration. But don't know why does it mean? What are the importances of it? Is it similiar to centre of mass?
0
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1answer
60 views

Moment of Inertia and Linear Dimensions

For similar solid bodies made from constant density, how does the Moment of Inertia about a particular axis vary with linear dimensions? This is from an school textbook. I have covered all of MI ...
0
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3answers
155 views

Rotational Inertia of a Disc and Subsequent Acceleration

This is more of a conceptual problem as opposed to anything wrong with the maths! (I think/I hope! :) ) But essentially the problem states: imagine a circular flat disc of radius $R$ and of mass ...