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3answers
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Moment of inertia of 4 particle system

Four particles are connected by rigid rods of negligible mass. The origin is at the center of the rectangle. The system rotates in the $xy$ plane about the z axis with an angular speed of $6$ rad/s. ...
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3answers
53 views

Does angular momentum of a system whose Moment of Inertia is changing remains constant?

In this problem, the moment of inertia of system is increasing. Correct option given is (b) and it is argued that no external torque acts. But If moment of inertia is changing , there should be a ...
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1answer
29 views

Moment of inertia and gravity

Would the objects have moment of Inertia if there was no gravity? Because imagine a bar, if I put my hand at the center of the bar and rotate it, it would be easier than rotate the bar picking one ...
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1answer
37 views

Rotational Dynamics Question [closed]

An ice skater spins with her arms folded. When she extends her arms outward, what will happen to her angular velocity?
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1answer
15 views

Moment of Inertia for objects moving in a circle?

I have been treating objects moving in a circle as a hoop, where $I=MR^2$ and it's been working but I feel like it works for a different reason from what I'm thinking. How do you actually find the ...
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1answer
26 views

Pulley inertia momentum of inertia

Considering a pulley with some mass, or some friction, How can its inertia (or momentum of inertia) influence the tension on 1 rope? Which part of the rope is influenced? Before or after the pulley?
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5answers
55 views

Two identical disks pulled differently question (Kinetic Energy)

I am currently taking a basic physics course in college and I am having a bit of trouble on this problem that deals with rotational and translational kinetic energy. Let's begin: The question: The ...
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3answers
50 views

Rotation of rigid body with two different angular velocities

Consider a cylinder that rotates about a vertical fixed axis with angular velocity $\vec{\Omega}$ while rotating about a vertical axis passing through its center of mass with angular velocity ...
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1answer
28 views

Principal axis of inertia parallel to the ones passing through the center of mass

Consider a rigid body and the (at least) three axes of inertia passing through its center of mass. Will any other axis not passing through the center of mass but parallel to one of the principal axes ...
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1answer
41 views

Parallel axis theorem and Koenig theorem for angular momentum

Are the parallel axis theorem and the Koenig theorem for angular momentum linked with each other in rigid body dynamics? The parallel axis theorem states that $$I_{z}=I_{cm}+ma^2$$ Koenig theorem ...
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1answer
38 views

Why is the center of mass frame always used in rigid body dynamics?

In most of the cases the center of mass is chosen for rigid body motion description, but this is not an obliged choice, since the motion of any point $P$ of the rigid body can be seen as the ...
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2answers
38 views

Disk let free to rotate

A rigid body moving with no constraints, in particular rotating, will rotate necessarily about a principal axis of inertia. I thought that the reason of this is that otherwise, the angular momentum ...
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1answer
38 views

Principal axes of inertia of a compound pendulum

I am confused about principal axes of inertia. Consider the compount pendulum in the picture, made of a rectangular plate. I oscillates about a horizontal axis $\hat{a}$ passing through $A$. The ...
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4answers
60 views

What is the moment of inertia really?

Is moment of inertia or second moment of inertia, simply the resistance of a body to rotate it over an axis? What is radius of gyration? What if the axis is via the center of mass or somewhere ...
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0answers
13 views

Torque required to rotate a drum in horizontal position with loose load

I am constructing a low heat drum dryer for fermented cocoa beans and am using a HDPE plastic drum of dimensions 610 mm diameter, 910 mm length and 200 litres volume. Thickness of the wall of the drum ...
2
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2answers
45 views

Meaning of parallel axis theorem: why is the moment of inertia minimum if the axis passes through the CM?

From parallel axis theorem follows that, given a rigid body, the moment of inertia is minimum if calculated with respect to an axis passing through the center of mass. What is the physical meaning of ...
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0answers
56 views

Kinetic energy of rotating rigid body

Sorry for boring you my friends. I am haunted by a problem of kinetic energy of rotating rigid body. Usually, the kinetic energy is calculated in the attached body reference. Because we could take the ...
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1answer
45 views

Inverted Pendulum dynamic eqution [closed]

I'd be glad to have some assistance with following one: According to my torque equation, I'm getting following one ($\theta$ is small angle and therefore approximation) \begin{array}{l} I = {J_c} ...
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2answers
69 views

What is Moment of Inertia of a cube about an axis passing through its centre and perpendicular to one of its faces?

Give a solid cube of uniform mass distribution and total mass $M$. I want Moment of Inertia of this cube about an axis passing through its centre and perpendicular to one of its faces where a is the ...
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1answer
38 views

Problems with moment of inertia [closed]

I totaly confused with these two problems can someone give any hints, or just final formula i get tired with it. Find the velocity of (a) a cylinder and (b) a ring at the bottom of an inclined plane ...
0
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1answer
29 views

Moment of inertia of two linked disks [closed]

It is an easy exercise but I'm not seeing it. I'm asked to find the moment of inertia of two equal disks linked together in such way that one is horizontal and the other one is vertical. I tried ...
2
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1answer
41 views

Moment of Inertia of Square Lamina [closed]

I know how to compute this using an integral. However, I was told that I could derive this as well by placing 4 squares together of moment of inertia $$I=kmr^2$$ and derive it again but I'm not sure ...
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0answers
53 views

Moments of inertia of composite area - xaxis [closed]

struggling with this question. Got the a) ( y¯ = 3.79 in )but can't seem to get b) a) Locate the centroid y¯ of the composite area. b) Determine the moment of intertia of this area about the ...
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0answers
51 views

Moment of inertia tensor of cube with objects inside

I'm currently trying to write a simulation that, essentially, calculates the moment of inertia of a hollow cube in 3D, where it's possible to attach additional cuboid shapes inside of it - to see how ...
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1answer
51 views

Parallel axis theorem proof?

First, I thought theorems do not have proofs. Anyway, for parallel axis theorem, I was given that the addition of translational kinetic energy and rotational kinetic energy proves the parallel axis ...
0
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1answer
36 views

Clarification on what inertia and area moments?

This is something I have never understood despite applying the formulas in many classes. What I'm hoping to find here is some clarification. My understanding is that the first moment of inertia is ...
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1answer
41 views

Where does the formula for the moment of inertia come from?

I think I 'understand' the concept of moment of inertia, but I don't see why it is proportional to r^2 (for a given point). Is the equation just empirical?
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1answer
38 views

Finding moment of inertia of a *double* rotating sphere

I'm completly stuck here: my system consist of a sphere rotating in a ring. How do I calculate the moment of inertia of this system? I know the MOI of a sphere rotating around it's cog, but here, I ...
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0answers
48 views

A Solid sphere rolling down an incline - find its radius

A solid sphere ( I = 2⁄5mr2 ) with unknown radius and 3 kg mass is rolling at 8 m/s. It travels 4 meters distance on a 30 degree ramp. What is the radius? This was given as a "trick" question ...
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0answers
27 views

resource recommendation for understanding moment of inertia

I'm a student majoring in mathematics and have to study mechanics this semester .I had problem in understanding concept of moment of inertia. So is there some nice place from where I can understand ...
0
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1answer
34 views

The dot product integral in the proof of the Parallel axis theorem

The first picture is a question about proving the Parallel axis theorem and the second is the solution. I have no problem with the solution except for the part which says that $$ \int 2\vec h ...
3
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1answer
27 views

Diagonal of a thin rectangular foil, inertial principal axis?

I'd like to know if the diagonal of a thin foil is an inertial principal axis. I know that if an axis isn't a symmetry axis then it isn't a principal axis. In the rectangle the diagonal isn't a ...
2
votes
2answers
73 views

Two particles have the same linear momentum but their angular momentum differ. Which's harder to stop?

Which one is harder to stop, a 2 kg particle moving in a circular path of radius 5 m , with angular velocity of 10 rad/s or a 2 kg particle moving in a circular path of radius 2 m with a angular ...
1
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1answer
99 views

How do I calculate the moment of inertia with velocity? [closed]

How do I calculate a total moment of inertia when I have point mass with velocity? It looks like this: If I understand correctly, firstly I have to find a center of mass. What do I do next?
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2answers
54 views

Moment of inertia of a body

I found the relation,$I=2\cdot T_\text{rot}$, where $I$ is the moment of inertia and $T_\text{rot}$ is the kinetic energy of rotation. Does moment of inertia depend on angular velocity? If it depends, ...
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1answer
42 views

How to calculate the moment of inertia of a 2 point mass system

I have 2 point masses $m_1$ and $m_2$ connected via a massless rigid rod to a center. $m_1$ is at the distance $r_1$ from the center and $m_2$ is at the distance $r_2$ from the center. How would i ...
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0answers
46 views

Parallel axis theorem non-uniform density [closed]

The parallel axis theorem says that if the moment of inertia of a body rotating about the body's centre of mass is $I_{cm}$, then the moment of inertia of the body rotating about an axis parallel to ...
3
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1answer
60 views

Moment of inertia meaning?

Why is the formula for calculating the moment of inertia this integral $$ \int r^2 dm~? $$ I understand the way we derived this formula from looking at the distribution of kinetic energy of a ...
0
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1answer
110 views

How do momentum get transferred?

Simple Question , Consider two objects namely $A$ and $B$ where $B$ is stationary and $A$ is moving towards $B$ with velocity $v$. When the two objects touch each other what does actually happen ...
1
vote
4answers
71 views

moment of inertia when a shape is cut [closed]

A disk of radius $r_1$ is cut from a disk of radius $r_2$, $(r_2>r_1)$ from the middle of the bigger disk . If the annular ring left has mass $M$ then find the moment of inertia about the axis ...
0
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1answer
23 views

If $z_G$ is a principal axis that goes through the center of mass, are every other axes $z$ parralel to $z_G$ also principal axes?

I know that : If $y$ is a principal axis $\iff$ you can express the angular momentum with respect to a point $Y$ on that axis (if the solid is rotating around that axis of course) with the formula : ...
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2answers
53 views

Calculating moment of inertia if a solid Sphere, using infinitesimally small spheres

Consider a Sphere of mass M, and volume V = (4/3)π(r)^3 and uniform density p, If I want to get its moment of inertia around an axis running through its centroid then I shall Integrate (dm r^2) And ...
0
votes
1answer
63 views

Moment of inertia of orbiting sphere

Is the moment of inertia of a sphere orbiting some object equal to the moment of inertia of a point mass at the same distance away from the object?
2
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2answers
81 views

Calculating moment of inertia for a cylinder?

I'm trying to calculate the moment of inertia for a cylinder about a longitudinal axis, but I don't know where I went wrong with my approach. $$I=\int r^2 dm$$ Assuming constant density: ...
3
votes
1answer
121 views

Parallel axis theorem: adding mass

I'm going through a worked physics problem and have a question about the parallel axis theorem regarding only adding mass while not changing is axis of rotation. Here is the problem: A physics ...
1
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1answer
98 views

Is moment of inertia numerically additive?

NOTE: The following argument is being made for square only, not any general shape. We have this square plate: From Perpendicular Axis theorem, $$I_1 + I_2 = I_z \\ I_3 + I_4 = I_z$$ Also, ...
3
votes
4answers
135 views

Can a die be made unfair without changing the center of mass or the exterior?

This question came from trying to design some 3d printed dnd dice. I think it's possible to make a die unfair without changing the center of mass or affecting the exterior shape*, but I'm not sure ...
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2answers
526 views

Moment of inertia of solid cube about body diagonal

How do I find the above mentioned moment of inertia? Steps I've tried: 1.) Triple integrations that proved to be to big. 2.) I noticed that the if we split a $2\times 2\times 2$ into individual ...
0
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1answer
154 views

Rotation of fluid filled cylinders [closed]

Given two cylinders of same mass , one completely made out of solid metal and the other a hollow one which has been filled with a viscous fluid say oil. Both have the same mass.Now if they are placed ...
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1answer
71 views

Second moment of area in parallel axis theorem

In parallel axis theorem why Ig second moment of area on axis passing through centre of gravity, is not zero. Even distance between axis and centre of gravity is zero.