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-1
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0answers
29 views

What will be the new moment of inertia? [on hold]

Let assume we have a sphere of radius $R$, and we can simply calculate the moment of inertia if we consider the axis is going through the center O. Let's cut a sphere small radius $r$ from the sphere ...
-4
votes
0answers
29 views

Moment of Inertia of a curved part of a graph [closed]

How to find the moment of inertia of a curve about a given axis. For example : How can we find the MI of the curved part of :$$\sin x\ $$ EDIT: Assume the range from $$[0 ,2\pi ]$$ and the axis to ...
5
votes
1answer
71 views

Compute an object's inertia around an arbitrary axis, using its known values for the x, y and z axes

I need to input inertia data into a bio-mechanical simulation program. I can find inertia data for parts of the human body, around the normal axes. I know the parallel axis theorem, so I can compute ...
1
vote
2answers
63 views

How does mass affect slipping of a rolling object?

I experimented by rolling a cylinder down a tube and noticed that by increasing its mass, it's time taken to reach the bottom decreased. Found out that mass doesn't actually affect the time taken, ...
2
votes
2answers
54 views

Inertia matrix in skew coordinates

One has, let's say, the inertia matrix of an object about it's center of gravity: $I_p$ in the coordinate system ($i, j, k$). What is the inertia matrix in another coordinate system, say ($i_1,j_1, ...
1
vote
2answers
51 views

Homework: Angular Acceleration from Net Torque [closed]

I have the correct answer but don't know how that is the correct one. My answers were way off which indicates I am missing something big but don't know what. Now the 4 torques are: t1=6.175, t2=....
0
votes
1answer
30 views

Moment of Inertia of a Cylinder with Cavity [closed]

Well, I have to calculate the moment of inertia of a cylinder that has radius $R_1$ and the cavity $R_2$. I tried doing just as you calculate the moment of inertia of a solid cylinder but instead of ...
1
vote
0answers
27 views

A trio of spinning marbles

My little brother showed me this devised act in which he stuck three marbles in a triangular pattern When he spun any of those marbles, the triplet would first rotate normally, but moments later, ...
3
votes
1answer
41 views

Interpretation of Moment of Inertia Tensor [duplicate]

Is there a simple physical interpretation for the off-diagonal entries of the moment of inertia tensor? I know that those entries are de facto necessary to use the tensor to calculate quanties like ...
-4
votes
2answers
52 views

Moment of inertia of the sphere [duplicate]

know the moment of inertia for both a solid sphere and a hollow sphere is , but my teacher has derived a moment of inertia of the sphere but am not sure about what axis she was deriving it , and she ...
-3
votes
2answers
47 views

Moment of inertia of a sphere

Moment of inertia of a solid sphere is $\frac{2MR^2}{5}$ and that of a hollow sphere is $\frac{2MR^2}{3}$ , but what does ($\frac{3MR^2}{5}$ ) represent to a sphere . On my notebook it is said that ...
2
votes
2answers
46 views

What's behind the moment of inertia and other “body-global” properties of bodies?

I'm an electrical engineer currently doing some (computational) mechanics stuff. In introductory literature about mechanics, you can read plenty about the moment of inertia and how you use it in ...
0
votes
1answer
24 views

Balancing an object with two loads

Suppose a bar (black) sitting on a suspended ball (blue) has two rigid loads of equal weight attached to it (red): Will the ball balance on the blue ball given even when the connection points of ...
1
vote
0answers
36 views

Dampening a swinging mass

Suppose a bar (black) sitting on a suspended ball (blue) has two rigid loads attached to it (red, green): Because the bar sits on a ball, the bar can swing clockwise or anti-clockwise. Suppose the ...
0
votes
1answer
40 views

Area moment of inertia about the y-axis for a triangle [closed]

I have a triangle which I have divided into two smaller triangles. Now I'd like to compute the area moment of inertia about the y-axis for the blue triangle. I've set the origin in the bottom between ...
0
votes
0answers
26 views

Moment of inertia of wheel-and-dart system

The problem I'm currently struggling with is: A wheel of mass M (assumed to be concentrated at its rim) and radius R is mounted horizontally so it may turn without friction on a vertical axle. (i.e. ...
0
votes
0answers
46 views

Natural Frequency and Inertia Tensors

The natural frequency of an oscillating object attached to a torsional spring is obtained by $\omega _n=\sqrt{\frac{k}{I}}$ In the case of single DOF motion, the moment of inertia is simple. ...
1
vote
1answer
98 views

Moment of inertia of trapezium

I have a trapezoidal and homogeneous lamina with mass m and ABCD vertices, on an xy plane. AB is the minor base, CD is the major base and AC is the height, with AB=AC=L and CD=2L. So basically I have ...
0
votes
3answers
51 views

What does the “moment” in the moment of force or the moment of inertia refer to? [duplicate]

According to the Merriam Webster dictionary: Moment - a very short period of time Does the word "moment" in quantities like the moment of force or moment of inertia refer to this colloquial ...
1
vote
3answers
77 views

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. ...
2
votes
3answers
117 views

Does angular momentum of a system whose moment of inertia is changing remains constant?

An equilateral triangle $ABC$ formed from a uniform wire has two small identical beads initially located at $A$. The triangle is set rotating about the vertical axis $AO$. Then the beads are released ...
0
votes
1answer
39 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 ...
0
votes
1answer
23 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 ...
0
votes
1answer
33 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?
2
votes
5answers
64 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 ...
0
votes
3answers
82 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 $\vec{\...
0
votes
1answer
39 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 ...
2
votes
1answer
57 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 ...
1
vote
1answer
48 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 ...
0
votes
2answers
48 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 $\...
0
votes
1answer
50 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 ...
0
votes
4answers
65 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 ...
0
votes
0answers
48 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
votes
2answers
70 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 ...
0
votes
0answers
61 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 ...
1
vote
1answer
62 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} +...
1
vote
2answers
114 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 ...
0
votes
1answer
40 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
votes
1answer
33 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
votes
1answer
66 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 ...
1
vote
0answers
87 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 ...
0
votes
0answers
70 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 ...
1
vote
1answer
66 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
votes
1answer
41 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 ...
0
votes
1answer
51 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?
0
votes
1answer
44 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 ...
0
votes
0answers
58 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 ...
0
votes
1answer
39 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 \cdot \...
3
votes
1answer
29 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
77 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 ...