The tag has no wiki summary.

learn more… | top users | synonyms

1
vote
1answer
23 views

Moment of inertia of a sphere

I'm looking at sample calculations of moment of inertia of a sphere here. In the first example (disc method), it has the integral as $dI = \frac{1}{2}r^2 \,dm$, while in the second example (shell ...
0
votes
2answers
97 views

Is it possible to calculate how fast something will roll down a hill?

If I have a wheel, I know it's mass and diameter and the slope of a hill. Can I calculate the time it will take to get to the bottom of the hill? I am doing a project for my science fair and I sent 5 ...
1
vote
1answer
62 views

What is wrong with this derivation of moment of inertia of a sphere?

I know the moment of inertia of a solid sphere is $\frac 2 5 MR^2$, but I keep getting $\frac 3 5 MR^2$ when deriving it: For a sphere of mass $M$ and radius $R$, $$\rho = \frac {M}{\frac 4 3\pi ...
2
votes
3answers
48 views

Instantaneous angular momentum of a disc

Suppose we have a disk of radius $r$ and mass $m$ travelling at velocity $v$. I want to calculate the instantaneous angular momentum with axis through the edge of the disc (on the circumference). ...
0
votes
2answers
68 views

Tensor of inertia of a hollow cube

I have found the tensor of inertia of a rectangle of sides $a$ and $b$ and mass $m$, around its center, to be $$I_{11}=ma^2/12,$$ $$I_{22}=mb^2/12,$$ $$I_{33}=(ma^2 + mb^2)/12.$$ All other elements of ...
0
votes
0answers
50 views

Calculating Inertia Tensor with Parallel Axis Theorem

Say you have a solid you are approximating as n point masses at different points in a 3D space. Each point mass has a mass of 1. The origin is not the center of mass. All the points have location ...
0
votes
2answers
41 views

If a paper disc is cut into a spiral, does its moment of inertia change?

It is obvious that there is no change in the mass of it and its radius. But the shape of the object does change. Does it mean its moment of inertia will also change?
1
vote
1answer
52 views

Why is second moment of area often referred as moment of inertia?

In many references, mostly civil engineering, the second moment of area is referred as Moment of Inertia. Is that "really" correct? From my understanding, moment of inertia is analogous to mass in ...
1
vote
1answer
377 views

How to calculate the moment of inertia of a solid cube

How do I calculate the moment of inertia of a uniform solid cube about an axis passing through its center of mass? I also wanted to know if the moment of inertia ...
19
votes
8answers
4k views

Why is the moment of inertia for a hollow sphere higher than a uniform sphere?

I have completely no idea and I am inquiring about this as it is an interesting question that popped in my head while doing physics homework.
4
votes
2answers
154 views

Angular momentum in a rod rotating around one end?

Sorry if I can't get straight to the point, I have to give a lot of details before I actually state the question. The formula for angular momentum is $L=I \omega$. If we look up $I$ for a thin rod ...
0
votes
0answers
71 views

Finding moment of inertia from Lagrange equation

I'm getting the following information: Consider a system consisting of two rotating bars of length $\ell$ and with uniform mass density and each with total mass $m$. The bars are attached to a common ...
1
vote
0answers
49 views

Moment of Inertia in SR/GR & Calculating it in General

In classical mechanics you want to calculate the moment of inertia for hollow & solid: lines, triangles, squares/rectangles, polygons, planes, pyramids, cubes/parallelepiped's, circles, ellipses, ...
1
vote
0answers
45 views

Rolling in 3D using Torque, Angular Momentum/Velocity

I'm stuggling to get a simulation working correctly. Below you can see what I am attempting to do. You can also view it here. Can you spot where I'm going wrong? (Calculated at start) 1) Inertia ...
0
votes
0answers
133 views

Tensor of inertia

The tensor of inertia of a solid sphere is $I_{ii}=\frac{2}{5}MR^2$ about an axis passing through its CM. Why would the tensor of inertia of each hemisphere about that axis be ...
1
vote
1answer
284 views

What is happening to rotational kinetic energy when moment of inertia is changed?

I know this question is asked here a lot, but I just had to ask this to finalise the concept. When a system lets say a rod of length $L$ and mass $M$ is rotating with angular speed $omega_1$ its ...
0
votes
0answers
32 views

The inertia tensor is “global”, how do I make it local?

A solid cuboid has the following moment of inertia: $$I= \begin{pmatrix} \frac{1}{12}h^2+d^2 & 0 & 0 \\ 0 & \frac{1}{12}w^2+d^2 & 0 \\ 0 & 0 & \frac{1}{12}w^2+h^2 ...
0
votes
0answers
63 views

Total energy of a rotating body?

I've no problems with the first part. However, I'm struggling with the last part of the question. The first thing I did is to find the a new moment of inertia for the whole system including the ...
0
votes
1answer
370 views

How do I calculate the experimental and theoretical rotational inertia of a point mass?

I'm getting some weird results from a calculation I'm doing and quite honestly, I'm pretty sure it's my fault. I do have an apparatus involved for the experimental process for my lab but I don't think ...
-1
votes
0answers
49 views

Moments of inertia [closed]

A compound flywheel is to be constructed in the form of a circular disc with a radius of 0.25m, a thickness of 0.05m and a moment of inertia about its axis of 2Kgm2. the flywheel is to have a ...
0
votes
1answer
122 views

Area moment of inertia of regular $n$-gons over polygon center $O$

Is it possible to consider the regular polygons ($n$-gons) as deformed circles and use a pseudo-polar coordinate system to calculate their moment of inertia over its center $O$. Inasmuch as I know (I ...
0
votes
0answers
118 views

Principal axis of inertia

I have these two questions: Determine: The principal axis of inertia. The maximal and minimal inertia's with respect to the principal axis. What is the principal axis of inertia? isn't it the ...
0
votes
2answers
301 views

Between a solid and a hollow cylinders of the same mass, which one has the greater rotational kinetic energy?

I know that rotational kinetic energy is $\frac{1}{2}I\omega^2$. Therefore, the rotational kinetic energy will depend on the moment of inertia. I came to the conclusion that since both have the same ...
4
votes
3answers
235 views

Moment of Inertia, why $r^2$and not $r$?

So my engineering mechanics book includes a brief discussion on area moments of inertia. Unfortunately, the ensuing chapter is predominately computational in nature. I don't have a thorough grasp of ...
0
votes
2answers
211 views

Will larger balls make a Newton's cradle swing more stable?

I got a rather small Netwon's cradle and when I start it, the effect is not very good since all the balls start to swing where the effect we want is obvious. The balls are small and I wonder if larger ...
1
vote
2answers
134 views

Determining the neutral axis of an I-shaped cross section with dissimilar materials

Determine the neutral axis of the I- shaped cross section with dissimilar materials. The top rectangle of the cross section is made out of aluminum and the second and third part are titanium ( these ...
0
votes
1answer
380 views

Derivation of Moment of Inertia and centre of mass?

In the equation above for the MI for a rod, why are we taking the limits from -l/2 to l/2? And why doesn't the integral doesn't include the centre of mass?
0
votes
2answers
168 views

Moment of inertia around two axes

In the this chapter of an online pdf we are given an equation for the deflection of a beam: $$\frac{d^2y}{dx^2}=\frac{\overline{M}}{E I}$$ where $E$ is the modulus of elasticity, $\overline{M}$ is the ...
1
vote
0answers
254 views

Rotational inertia of a sphere and a cube? [closed]

Can someone explain which would have more rotational inertia, a sphere or a cube, and why? Suppose they have the same mass, the side of the cube is equal to the diameter of the sphere, and the cube's ...
1
vote
1answer
405 views

Moment of Inertia and Rotational Dynamics? [closed]

I'm having problems with the intuition behind the Parallel axis theorem and the Perpendicular axis theorem. I'm self studying Mechanics for the British Curriculum but, the book I've is missing the ...
2
votes
1answer
369 views

Moment of inertia of rotating particles in center of mass frame?

I am trying to simulate a collision between two molecules. I know the energy for every position/orientation, from which I can calculate the forces. The treatment is classical and the molecules are ...
0
votes
2answers
83 views

Moment of Inertia [closed]

Let $f(x) = \frac{1}{L}$ be a probability function, where $L$ is constant. Find the mean and variance. Discuss your results by making a connection to the moment of inertia definition.
2
votes
3answers
733 views

Moment of inertia of a planet

Is there a good way to directly measure a moment of inertia of the Earth, or say, other planet?
3
votes
1answer
160 views

Do higher-order mass moments have any physical meaning?

The zeroth moment of mass of an object is simply its total mass. The first moment of mass yields an object's center of gravity (after normalization). The second moment of mass yields an object's ...
0
votes
1answer
97 views

Rotational Hamiltonian for collective model

The effect of rotation can be considered by modelling the nucleus as a rotating body, characterised by some moment of inertia. Then how The Hamiltonian describing rotation is? ...
1
vote
0answers
143 views

Hamiltonian Nuclear collective model

Let $\mathscr{I}_3$ and $\mathscr{I}$ are the moments of inertia for rotations about symmetry axis 3 and about an axis perpendicular to it , and I is the angular momentum operator with components ...
-1
votes
2answers
1k views

Center of a mass of a hemisphere [closed]

How can I show that position vector of the center of a mass of a hemisphere is $(0,0,\frac{3a}{8})$ where $a$ is radius of a hemisphere, $x$ and $y$ axis are laying on the base and $z$-axis is ...
2
votes
2answers
286 views

conceptual doubt in method to find moment of inertia about an axis

I asked this question before about whether I can take a component of angular velocity along another axis and say that the body spins about that axis with that component. Now I have another doubt: ...
3
votes
3answers
456 views

Origins of Moment of Inertia

Where exactly does the equation $MR^2$ for moment of inertia come from? The quantity itself seems fairly arbitrary.
6
votes
3answers
1k views

What is the physical significance of the off-diagonal moment of inertia matrix elements?

The tensor of moment of inertia contains six off-diagonal matrix elements, which vanishes if we choose the principle axis of the rotating rigid body and the components of the angular momentum vector ...
5
votes
3answers
818 views

Moment of Inertia (triangular plate)

I want to generalize the formula for the MOI of a triangular plate (sides $a,b,c$) about an axis passing through mid point of one sides and perpendicular to it's plane . The mass of plate $M$ is ...
3
votes
2answers
808 views

First and Second Moment of Mass

I recently came across the definition of the Center of Mass of a system as the point about which the first moment of mass is zero. Further, it defined Moment of Inertia as the second moment of mass. ...
1
vote
1answer
635 views

Kinetic Energy And Rotational Motion

The problem is, "A metal can containing condensed mushroom soup has mass 220 g, height 11.0 cm and diameter 6.38 cm. It is placed at rest on its side at the top of a 3.00-m-long incline that is at ...
0
votes
1answer
676 views

Finding Rotational Kinetic Energy Of A Clock

The problem I am working on is: Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure ...
0
votes
2answers
3k views

Torque And Moment Of Inertia

I am reading the two concepts mentioned in the title. According to the definition of torque and moment of inertia, it would appear that if I pushed on a door, with the axis of rotation centered about ...
0
votes
1answer
2k views

Calculating Moment Of Inertia

The problem I am working on is: A uniform, thin, solid door has height 2.10 m, width 0.835 m, and mass 24.0 kg. (a) Find its moment of inertia for rotation on its hinges. (b) Is any ...
0
votes
1answer
454 views

Two Different Sorts of Inertia: Inertial Mass and Moment of Inertia

There are two different sorts of inertia: inertial mass and moment of inertia. I am currently reading about moment of inertia. Now, I know inertia is an important concept; with it, we can determine ...
0
votes
2answers
419 views

Moment of inertia of a football and its angular momentum

What are the ways to create a mathematical model for the moment of inertia of a football? Can the moment of inertia of the football be simplified to two cones stack against each other? I'm trying to ...