# Questions tagged [moment-of-inertia]

The moment of inertia, or rotational inertia, determines the torque needed for a desired angular acceleration about a rotational axis. Like inertial mass is the resistance to being linearly accelerated, the moment of inertial is the resistance to being rotationally accelerated.

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### Kinetic energy of a disc rotating about an inclined axis [closed]

What is the kinetic energy of a circular disc of mass M and radius R rotating with angular velocity w about an axis that is inclined to its surface by an angle of 45 degrees? (Please answer using the ...
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### Why does moment of inertia stop at 1/2 as solidness of a cylinder increases?

So I have two things about moment of inertia: The I for a hoop is $I=MR^2$ and the I for a solid disk is $I=\frac{1}{2}MR^2$ I've noticed that as "solidness" goes up from 0% (completely ...
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### How does the moment of inertia work in this physics question? (Vibrations and Waves by George C. King) [closed]

Not sure if this is just me having a moment where I'm missing something totally obvious, but I'm going over some old undergraduate physics work to reinforce my knowledge, and I've encountered a step ...
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### Calculating the amount of torque applied to to stop a rod rotating at some angular velocity

Consider a Rod AB, having length $l$ with non uniform mass density $\lambda (x)$ a function of length from the end A, is rotating at an angular velocity $\omega$ with fixed end A and free end B. ...
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### What is the physical significance of Moment of Ineria about a point vs Moment of Inertia about an axis. In which types of problems we use the former?

I know the mathematical formula of both about an axis and a point. But where exactly we use moment of Inertia about a point. For 2d objects like discs rotating in its own plane, the moment of Inertia ...
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### What is the connection between moments in probability theory and the moment of inertia?

My question arises as the moment of inertia (MOI) has been described as a second moment. In my understanding if the MOI is indeed a second moment of a distribution of mass, this suggests the MOI could ...
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### Spinning top stabilisation for a type of aircraft/drone

Spinning tops use gyroscopic precession to be able to stay upright whilst spinning. Would it be possible to use this phenomena to create a flying craft that would be stabilised by gravity and the ...
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### How can we choose two different mass moment of inertias for the same momentum calculation?

I am working on answering part (a) and here is what I got: By conserving linear momentum, we have that $$mv_0 =(3M)v_f \hspace{3mm}\implies \hspace{3mm} v_f =\frac{1}{3}v_0$$ Now, in order to conserve ...
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### Moment of inertia about a non-fixed axis

Let’s say I have a cubical shape of mass M and sides s rotating about a vertical axis placed at distance D from the cube’s center of mass. Its moment of inertia I under these conditions is equal to: I ...
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### Proof for Moment of Inertia of Triangle (with respect to the axis out of the page at a origin) [duplicate]

I found a formula for a "Triangle with vertices at the origin and at $P$ and $Q$, with mass $m$, rotating about an axis perpendicular to the plane and passing through the origin" given on ...
1 vote
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### Is there a maximum angular acceleration due to gravity for a given radius?

I'm having trouble understanding the relationship between angular acceleration and tangential acceleration, specifically, how can an angular acceleration created by the tangential acceleration of ...
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### To find angular momentum of a circular hoop [closed]

A circular hoop of radius 0.3cm has moment of inertia 0.09 kg-m^2 about its axis, makes 10 revolutions per second. Find its angular momentum about its axis and the force that increases the angular ...
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### How to compute inertia tensor off the center of mass with geometric algebra?

I was reading Doran & Lasenby's Geometric Algebra for Physicists when I stumbled upon this, where $\mathbf{a}$ is a vector taken form the centre of mass. Returning to the definition of equation (...
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### What is the moment of inertia $I$ when angular velocity $ω$ is zero?

$$I = \dfrac{L}{\omega}$$ What is the moment of inertia when $\omega = 0$? Is it just not defined or is the formula not valid when $\omega = 0$?
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### Does the direction of an angular velocity vector always stays constant with no force involved [duplicate]

Are there cases where there is a rigid body that rotates somehow and the direction of the angular velocity vector changes in the lab system?
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### Confusion about calculating Moment of Inertia of hollow sphere

A hollow sphere can be visualized as a stack of infinite rings varying in size, While calculating the moment of inertia of a hollow sphere, why does the following logic falter?: Assume compressing the ...
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### Finding the torque required to turn a cart resting on 4 wheels

I am building a cart that has two handles on the bottom face. The cart is basically a table resting on castor wheels, one on each leg. If I apply a couple on the handles, the cart will turn. I am ...
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### Nucleus with the largest deformation

I am learning some nuclear physics and got interested in deformed nuclei. Which nucleus has the largest deformation, and hence the best shaped rotational spectrum?
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### Physics Principle of Balancing Board

Consider one of these Typically, it is well known that having you legs further apart helps you balance better, the wider the base, the easier it is to balance. I guess a body with a larger base area ...
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### Time derivative of moment of inertia tensor

Suppose that I have some fluid in a fixed volume. Its moment of inertia is given by $I=\int\rho r^2dV$. The derivative of $I$ is given by $\dot{I}=\int\frac{\partial\rho}{\partial t}r^2dV$. Why do we ...
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### Created a resource to help solve a problem I was having in a lab. Can I publish it?

I had to complete a lab for school assessing the accuracy and precision of calculating a triangular prism’s moment of inertia using a trifilar pendulum. When I wanted to compare my lab results to ...
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### Computing rotational kinetic energy from first principles

I want to calculate the expression of the rotational kinetic energy of a rectangular plate when the axis of rotation does not go through the center of gravity from first principles. However, I am not ...
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### Combined KE for an object rotating about a point other than COM

I know the KE equation for combined translational and rotational motion, which is $K=Mv^2/2+I\omega^2/2$, and here $v$ is the velocity of COM and $I$ is the moment of inertia about the COM. But what ...
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### How to calculate torque at the end of a lever arm?

I am messing around with creating small computer simulations to self study. Last time I did physics was in high school. Consider the setup below. An electric motor (black) is spinning a metal disk (...
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### Moment of Inertia tensor confusion

This is the moment of inertia tensor about the COM. $$I_{ij}'=\sum_{k=1}^Nm_k\left[\vert\mathbf{r}'^{(k)}\vert^2\delta_{ij}-r_i'^{(k)}r_j'^{(k)}\right]\neq I_{ij}$$ I don't understand how to compute ...
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### Moment of inertia of a cantilever beam [closed]

As part of a project, I'm calculating deflection of a cantilever beam, something like the image below where the beam bends due to a load. To do so requires its moment of inertia, and I'm thinking of ...
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### Why does the rotational level spacing increase when moment of inertia decrease?

In the rigid rotor approach we obtain the result that the spacing between different rotational energy levels in a particular vibrational state is $\nu = 2B(J+1)$ and $B = \frac{ h }{ 8 \pi^2 Ic }$, ...
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### Moment of Inertia of Cylinder through horizontal axis [closed]

Regarding moment of inertia (MOI) of a solid cyclinder, I want to calculate the MOI through the horizontal axis (central diameter) which is the 2nd diagram in the figure: I want to do so by using the ...
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### Would a linear accelerating object be harder to rotate?

Imagine a cylinder-shaped rocket, rotating around an axis perpendicular to the axis of thrust with constant angular speed of w. The rocket starts thrusting after some time. No air pressure, no gravity....
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### Motivation behind Definition of Moment of Inertia [duplicate]

I was studying rotational mechanics a while ago, and came across the idea of moment of inertia. The moment of inertia of an object describes its resistance to angular acceleration. The definition of ...
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### Maxwell's wheel - moment of inertia vs damping coeff

I am investigating the relationship between the moment of inertia of a yoyo-like apparatus (maxwell's wheel) and its damping coeff. I am adding disks to my yoyo to change its moment of inertia, which ...
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### Why these derivations use different ratios to calculate dm and can they be done using another ratio?

My question is about the ways to derive these expressions. Why in the case of the thin circular plate dm = (M/A) * dA is used while in the thin rectangular plate dm = (M/V) * dV is used? Can they be ...
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### Moment of Inertia of a gyroscope

I saw that the moment of inertia could be calculated for bodies as the addition of the sum of their parts, so I was wondering if it could be calculated for the gyroscope that is pictured below I was ...
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### Weight and rate of movement

Im limited on my physics knowledge and sometimes can't understand simple laws. When i have two 5kg objects on a "manual weight scale" then forces are equal and the scale stays in place. ...
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### Moment of Inertia in the presence of strings [closed]

I've seen that in some problems when strings are present, to get the required answer, it is considered as if the string was not present and the mass being directly attached to the pulley/other body. ...
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### Confused with the effects of moment of inertia and torque

According to the definition of torque, if the distance from the pivot is large the force required to apply will be smaller to move with the specified angular velocity/acceleration. And we can ...
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### Doubt regarding the moment of inertia of a rod [closed]

In this system, I am calculating kinetic energy as: $$T = \frac{1}{2}I_{O}w_{O}^2 + \frac{1}{2}I_{G}w_{bar}^2 + \frac{1}{2}v_{G}^2$$ Being G the center of mass of the rod AB. Note: A is not fixed. ...
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### Doubt in parallel axis theorem exercise

My teacher solved a parallel axis theorem in class and I don't understand one of the steps he did The exercise consists of a coin of mass $m$ and radius $r$ moving on circles inside of a cone, the ...
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### Why are 2D inertia tensors $2\times 2$ matrices when 2D objects can only rotate around one axis?

Why is the 2D inertia matrix defined as $$\begin{bmatrix}I_{xx}&I_{xy}\\I_{yx}&I_{yy}\end{bmatrix}$$ and not just a vector 2 or scalar? I saw something saying that $I_{xx}$ is the moment of ...
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### Calculate rotation from net torque and inertia matrix

I am trying to grasp the concepts of forces applied to a rigid body resulting in a net change of the rotation of the object. This is not a home assignment and I read some resources on both the web and ...
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### Conservation of Angular momentum for an irregular body rotating about three axes

I am having trouble understanding how conservation of momentum can be used to calculate final angular velocity for a body rotating in multiple axis with an asymmetrical MoI. Suppose a satellite is ...
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### Moment of inertia of a rolling cylinder

Here is the question: "A rigid body with a cylindrical cross-section is released from the top of a $30^{\text{o}}$ incline. It rolls $10.0 \, \text{m}$ to the bottom in $2.60 \text{s}$. Find the ...
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### Change in moment of inertia when a rotating body collides with another (static) body

My question is whether the moment of inertia changes when a body that is rotating around its center of mass (like a rod or a sphere) hits another static body (like the ground)? I assumed this could be ...
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### Doubts about the parallel-axis theorem

I was studying about the parallel-axis theorem but had trouble making intuitive sense looking at it's derivation and statement. My confusion is that how is the moment of inertia about the center of ...
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### How do you integrate a physics integral? [closed]

I've only taken Physics I (w/ calc) in uni, so physics is pretty new to me, and I'm only through Calculus 2. However, I keep seeing integrals like these everywhere in physics, and want to know how to ...
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