Inertia Definition and 1000 Threads

Homework Statement A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 3.3 kg and radius R = 0.26 m. The rods each have mass mr = 1.2 kg and length L = 0.72 m. What is the moment of inertia of each rod about the axis of rotation...

Homework Statement If you have data such as time of rotation when arms are extended and the lengths of their folded and extended arms measured from the centre of the skater. I know I1ω1=I2ω2 and can work out ω from the radius and time of rotation. Where can I go from here to estimate the mass...

Moment of inertia is I = MR2 object has more mass means more inertia and less mass means less inertia. That means moment of inertia is directly proportional to mass. But how the moment of inertia is directly proportional to the square of the distance.?

Homework Statement [FONT=Arial]A solid cube of wood with side 2a and mass M is resting on a horizontal surface. The cube is constraint to rotate about a fixed axis AB. A bullet of mass m and speed v is shot at the face opposite ABCD at a height of 4a/3. The bullet becomes embedded in the cube...

Homework Statement Let R be the solid region that is bounded by two spheres x^2 + y^2 + z^2=1 and x^2 + y^2 + z^2=2. Determine the moment of inertia of R around the x-axis if the mass density per unit volume of R is u=sqrt(x^2 + y^2 + z^2). Homework Equations Moment of Inertia around the...

Im needing to calculate the Zxx and Yxx for 2 shapes. The shapes are an H profile and a + profile however its not the basic profiles I am needing but the moment of inertia for the weld profile surrounding them as the theory is they are welded to a vertical metal surface then a load is applied...

Imagine that you are in a spacecraft and you then open a hatch, of a type like the door of a Gemini capsule (it hinges outward). Does the action of the hatch opening outward then hitting a stop impart force to the ship? Note that this is in deep space, that is, ignoring outside gravity fields...

Homework Statement The mass of a homogenous thin plate is 36kg. Determine it moment of inertia about the x axis Homework Equations Parallel axis theorem: Ix = Ix' + d^2*m The Attempt at a Solution p = m/a = 36/0.36 = 100 Because the density is homogenous, I found the mass of the first...

Hi, it's been quite some years since I took some entry-level mechanics at uni, and my book is no longer with me, so I'm struggling a bit here. I'm making a very simple rigid body simulator just for fun, but the angular velocity is not working out right. I suspect I've forgotten something...

Is there any difference between mass and inertia? Is the word "inertia" necessary, or could it be eliminated from physics books?

Problem: Consider an ice skater spinning in a circle. We will approximate the body as a cylinder with a radius of 0.25 m. The total mass of the skater is 50kg. When the skater has her arms extended we will approximate her body as a cylinder with two rods attached. Each arm is 0.75 m long and has...

Homework Statement Hi everyone, I need some help to know how to find the components of the inertia tensor matrix of a rigid body formed by a gruop of point masses attached to bars with no mass. I have 3 masses with cartesian coordenates: 1 (a,a,0), 2 (a,0,0) and 3 (-a,-a-0). The...

I'm reading an old engineering book about aircraft Structures from the 1950s and I don't recognize the term inertia load. Can anyone give me a definition of it? I'm going to take a guess based on what i do know. Inertia is a body's resistance to change in speed and direction. So when some...

A small confusion ! Why is most of the mass of the wheel concentrated on the rim ? I know that it is to increase the moment of inertia , but what is the practical use of doing so ? Thanks in advance !

Hello, I am curious regarding the forces other than the pressure created by combustion process in IC engine.Whether inertia and friction affect worth considering or not, I want to know magnitude and nature of these forces and their effects On efficiency and performance.Thank you...

I've done many exercises about inertia tensors of 3D bodies and sticks but now I have this exercise and I got stuck without any idea of how to do the integration to compute the inertia tensor. The statement is this: "Compute the inertia tensor of a cross-hanger consisting of 3 thin and linear...

For a uniform, hollow cylinder, why is this derivation wrong? M = mass of whole solid cylinder m = mass of missing cylindrical piece R = radius of whole cylinder r = radius of missing cylindrical piece moment of inertia = moment of inertia of whole cylinder - moment of inertia of...

Why do we use inertia in rotational motion and not the whole mass of an object ?

The Question : A cylinder of mass M , and moment of inertia around its center Io, is initially rotating around its central axis with angular velocity wo. İt is gently placed on a homogeneous thin plate of mass m which rests on a smooth horizontal surface. Assume that the plate is sufficiently...

I would like to know if there is any proof as to whether the moment of inertia for two bodies (the masses of each body are distributed on a line) about their respective center of masses, is strictly different. If not, can anyone provide me a link to where the work is computed.

Homework Statement I found the moment of inertia of a rectangle, with the axis perpendicular and going through the center using double integration. But I also used what i thought to be an equivalent method, but it didn't work.Homework Equations dI=r^2dm \int dI The Attempt at a Solution I was...

1. Question: What is the moment of inertia of a thin, flat plate in the shape of a semicircle rotating about the straight side (Fig. 12.28)? The mass of the plate is M and the radius is R The diagram is attached for reference. Homework Equations Moment of Inertia: I = ∫R2dm...

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[SIZE="4"]Definition/Summary Inertia is the phenomenon that a force is required to cause change of velocity. The amount of inertial mass of an object is measured by measuring how much force it takes to accelerate it. The symbol for inertial mass is m. [SIZE="4"]Equations...

Good morning PF, I am having some difficulty finding info on calculating a composite moment of inertia. The section I am working with is 8 separate columns (WT5x15) arranged evenly spaced around the circumference of a circle. You can see what I'm taking about in the attached jpg. I found...

Homework Statement since it's asking us to find the moment of inertia with respect to y-axis, why did they draw the differential element to x-axis? Homework Equations The Attempt at a Solution because of the initial problem.. i don't know how to start.. so dA = x dy I(y) =...

Homework Statement Suppose I have a rod with a know length, L, and 2 point-liked mass with know mass, m, each of them are fixed at both ends of the rod. And the rode has an axle connected at its midpoint where the axle is connect to a circular spring. The rod(with the 2 mass) is rotated 180...

Hi. I'm designing what effectively is a large door on hinges. The door has the following properties Mass = 336 kg Width = 1.8m The door rotates from closed position through 45deg to open position. In order to 'control' or damp the rotation of the door, I'm fitting a 3Nm friction clutch on...

hello, I am trying to find the new moment of inertia total for a rectangular stainless steel 4"x2"x.25"thk with a 3"x.75" flat bar welded on top of the short side of the rectangular tube. The short side (.75") of the flat bar will be welded to the center of the rectangular tube to the 2"...

Homework Statement Two children on opposite ends of a merry-go-round of radius 1.6 m throw baseballs at the same speed of 30 m/s but in opposite directions as shown. The mass of each baseball is 0.14 kg, and the moment of inertia of the merry-go-round and children combined is 180 kg-m^2. If...

As it's stated in Newton's law of gravitation, every object with mass attracts all other object with a force which causes acceleration. So basically there are infinite number of forces in our universe which affect our planet as well. My question is, can an inertifal frame (which has the net...

I am curious to know the various opinions, what ideas you favor as to the cause of inertia? What could the reference frame(s) be that induces inertial effects, and how could those effects be caused? Could the reference frame be absolute space as Newton thought, or the more relativistic idea of...

The following equations are found in the following reference (Page 119): http://www.eeh.ee.ethz.ch/fileadmin/user_upload/eeh/studies/courses/power_system_dynamics_and_control/Documents/DynamicsPartI_lecture_notes_2012.pdf By definition, the inertia constant for a synchronous machine is...

Homework Statement A uniform cylinder 20 cm long, suspended by a steel wire attached to its mid-point so that its long axis is horizontal, is found to oscillate with a period of 2 seconds when the wire is twisted and released. When a small disc, of mass 10 g, is attached to each end the...

Homework Statement Three small spherical masses are located in a plane at the positions shown below. The masses are Q=0.700 kg, R=0.400 kg, and S=0.800 kg. Calculate the moment of inertia (of the 3 masses) with respect to an axis perpendicular to the xy plane and passing through x=0 and y=-3...

Homework Statement The Wikipedia article on spatial rigid body dynamics derives the equation of motion \boldsymbol\tau = [I]\boldsymbol\alpha + \boldsymbol\omega\times[I]\boldsymbol\omega from \sum_{i=1}^n \boldsymbol\Delta\mathbf{r}_i\times (m_i\mathbf{a}_i). But, there is another way to...

Homework Statement "the question is included in the attachment" Homework Equations F=ks, E=stress/strain=(force/area)/(change in L/L) Second moment of inertia=I=(1/2)*base*height^3 The Attempt at a Solution Sice F=ks k=F/s where F=p and s= d(L) (change in L)...

Homework Statement The rotating parts of a motor have a moment of inertia of 15 kgm^2 and an optimum running speed of 1400 rev/min. When operating the motor is connected at optimum speed , by means of a clutch, to a shaft which has a counter rotation of 600 rev/min. The shaft has a mass of...

The rotating parts of a motor have a moment of inertia of 15 kgm^2 and an optimum running speed of 1400 rev/min. When operating the motor is connected at optimum speed , by means of a clutch, to a shaft which has a counter rotation of 600 rev/min. The shaft has a mass of 80 kg and a solid...

Homework Statement The thin, homogeneous bent rod has the mass m and the total length of 4b. It rotates with the angular speed of ω = ω0(24i + 12j - 6.0k) (only rotation) Determine the expression for the moment of inertia with consideration of the center of mass of the rod The figure...

Hi, I've just started Gravitation and Inertia by Wheeler and Ciufolini. This is really a sort of trasure to me, since I was looking for something about it since when I read Einstein's relativity papers, involving Mach's principle. The main point is really simple "Inertia here arises from mass...

Homework Statement A yo-yo is spun from rest by pulling on the string with a constant tension of 2.0 N. The radius of the inner rod on which the string is strung round is 0.50 cm. The tension is applied for 5.0 seconds after which the yo-yo is observed to spin with an angular velocity of 15...

When a particle is traveling very close to c. Will its mass actually increase and therefore its ability to resist change in its state of motion increase, OR will JUST its ability to resist change in its state of motion increase and the mass will remain the same? Will the particle just behave...

Homework Statement I have a practical coming up and I have to research the method and calculations. I will be given an irregular lamina that I need to use as a compound pendulum in an experiment to determine the gravitational acceleration, g, as well as the moment of inertia (Io) of the...

Homework Statement A mass m is tied with a light string,which it's another end is winded at a axle fixed at wall,in which it's radius is r. Assume there is no friction.The mass is released from rest and falls a distance S after time t. Find the moment of inertia of the axle.(represents I in...

Statics: If computing the moment of inertia about the y-axis of a triangular shape in the 2nd quadrant(not touching the x-axis); would i still use hb^3 /12

I am working on a lab that is meant to test the validity of (m1

Homework Statement The Earth is slightly thicker around the equator and hence $I_{0}\neq I_{\zeta}$ I am curious in finding the angular velocity for the **precession** between using the fact that the distance between the spin axis and the precession axis is 10 meters on the surface of earth...

Homework Statement A homogenous disk with radius R and mass m lies in the xy plane so its center matches the origin O. Point O' is on the z axis at a distance s from point O. Axis y' passes through point O' at an angle \theta with the z axis. Find the moment of inertia around axis y'...

Hi, I was just going over the moment of inertia for a 2D lamina, I've been happy with writing the small mass element dM as dM = ρdxdy where ρ is the area density, but for some reason decided on doing it like this, M(x,y) = ρxy so dM = \frac{∂M}{∂x}dx + \frac{∂M}{∂y}dy = ρ(ydx +...