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2
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0answers
23 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
votes
0answers
13 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
28 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
60 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
94 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
29 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
38 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
111 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
72 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
58 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
36 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
votes
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
78 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
59 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
67 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
vote
0answers
37 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
55 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
55 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
vote
1answer
80 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
51 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
44 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
61 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
68 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 ...
0
votes
0answers
134 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
vote
3answers
71 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
84 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
vote
1answer
76 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
39 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
108 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
votes
2answers
673 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
92 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
125 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
260 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
62 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
35 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
26 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
59 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
77 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
223 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
402 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
votes
0answers
120 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
70 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
votes
0answers
78 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 ...
1
vote
1answer
201 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 - ...
0
votes
3answers
188 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
vote
1answer
103 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
vote
0answers
76 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
votes
0answers
97 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
vote
2answers
201 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
votes
2answers
126 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 ...