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0
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2answers
33 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
42 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
51 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
26 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
56 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
36 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
36 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
70 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
27 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
23 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
votes
1answer
36 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
votes
1answer
75 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
votes
1answer
114 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
votes
2answers
31 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
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1answer
65 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
votes
5answers
140 views

Moment Of Inertia About Centre of Mass

Why is moment of inertia minimum about centre of mass of any rigid body?
1
vote
1answer
82 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
100 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
52 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 ...
18
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4answers
1k 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
109 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
82 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
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2answers
95 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
48 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
61 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} ...
1
vote
1answer
86 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
91 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
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0answers
65 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
53 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
86 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
86 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
votes
0answers
209 views

Boiled egg vs raw egg moment of inertia

I know that the acceleration of some body rolling down an incline with fixed inclination goes as $1/(k+1)$ where the moment of inertia of the body is $kmr^2$. I am trying to decide whether a raw egg ...
1
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3answers
86 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
95 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
126 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
votes
1answer
41 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
votes
3answers
121 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 ...
6
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2answers
696 views

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 - ...
2
votes
1answer
122 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
votes
2answers
143 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
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1answer
446 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
vote
1answer
65 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
vote
2answers
37 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
votes
1answer
38 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
vote
2answers
80 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
votes
1answer
105 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 ...
1
vote
4answers
285 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
518 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 ...
1
vote
1answer
138 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
vote
0answers
77 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 ...