Inertia Definition and 1000 Threads

Homework Statement Find the second moment of inertia of a rectangle. The Attempt at a Solution Anyone know why my answer is 4 times too big?

Hello again, I am currently designing a flywheel for a 745 KW engine inertia dyno. Basically my design requirements are so: Max RPM: 530 RPM (=55.5 rad/s) Flywheel Diameter: 1.7 meters Time needed to accelerate: 60 second (to max rpm) I need help determining the mass of the...

Homework Statement Hi, I have been asked to find the moment of inertia of a rolling ball. The ball can be any size and radius. I have chosen a solid ball. The experiment says that I should roll the ball down a ramp and then measure the time it takes for the ball to roll from the end of...

I am having trouble right now with the same problem (finding Ixx and Iyy). \begin{equation} I_{yy} = \int(x^2 + z^2)dm \end{equation} where \begin{equation} dm = \frac{2M}{R^2 + H^2} q dq \end{equation} and q is my generalized coordinate that is measured from the origin down the length of the...

KErotational = (1/2)Iω2 420 = (1/2)Iω2 420 = (1/2)I(402) 420/(402) = (1/2)I 0.2625 = (1/2)I 2(0.2625) = I 0.525 = I 0.53 = I

According to GR, the inertia of bodies is greater near masses. - https://en.wikisource.org/wiki/Geometry_and_Experience Has this been tested? I did not find a clear answer, the gravity tests seem to be testing other things. Can it be tested? Intuitively I think that it should be possible...

While this may seem like a silly question, I had difficulty answering it completely. "If space is a vacuum, why aren't we somewhere else already?" If it is truly empty, devoid of any substance or mechanism whereby it might restrain or compell the action of an entity, what keeps entities...

Hello everyone, (This might be a little long winded but I would very much appreciate some help on this!) Today while in psychology class, I was thinking about a much more important subject, namely a project I want to start working on. Basically what I want to do is build a motor from the...

Homework Statement Find the moment of inertia and center of mass of: A uniform cone of mass M, height h, and base radius R, spinning about its symmetry (x) axis. Homework Equations I = ∫R^2dm The Attempt at a Solution I tried using I =∫R^2dm, solving for dm I got dm=(M/V)dV...

Homework Statement [refer to picture, thanks] The "L-shaped" figure rotates on the axis which which intercepts through 9 kilogram and 2.5 kilogram masses. Find the moment of inertia of the object for this type of rotation. Disregard the masses of connecting bars. Homework Equations MR^2...

Homework Statement I was wanting to see if someone could check my calculations. I've checked out the Iy and Ix in Autodesk Inventor and what I got is wrong. Here are the links to my images. I apologize, the uploading option is not allowing me to upload the pictures...

Homework Statement An object with a mass of m = 5.10 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.250 m and mass M = 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center. The...

Homework Statement I was given a formula sheet that shows the moment of inertia equations for three shapes: rectangle, circle, and triangle. Homework Equations There seems to be two sets of MOI equations. Here are the rectangular equations: Rectanglular: Ix=\frac{bh^3}{3}...

hi everyone! I'm very confused about inertia matrix... i searched all over the web but didn't find a concise explanation of why it is useful to use it. What's used for ? When should i use it ? the wikipedia explanation is too formal and it's difficult for me to understand... so can somebody...

Homework Statement Consider a solid homogeneous object taller than its wide, with the top and bottom parallel. Prove that the shape with the lowest moment of inertia about an axis through the object is a cylinder with the axis through its axis of symmetry. density, mass, and height are...

Here's a derviation from HyperPhysics: He says: dV=πy^{2}dz However, if we're finding the surface area of the sphere: dA=2πRdz≠2πydz If we cannot use dA=2πydz, how come dV=πy^{2}dz is still applicable?

Hello guys, I am calculating Bending and Shear stresses in hollow beams. We have a particular kind of shell that we use for impact loading, so we put rubber discs around the steel shell. So my question is, how will it affect the moment of inertia ? Since I know that the rubber discs will...

Homework Statement A 1.3 kg block is tied to a string that is wrapped around the rim of a pulley of radius 7.2cm. The mass of the pulley is 0.31kg. The block is released from rest. If the velocity of the block is 3.0m/s after it falls 0.5m, what is the moment of inertia for the pulley?[/b]...

Homework Statement Question is about buckling, so i know i need to work out I (moment of Inertia), which is for a hollow tube. Homework Equations So the paper states..I = (0.08^4 - 0.06^4)∏/64 = 1.37 x 10^-6 m4 When i do that on my calculator, i don't get this answer. Puzzled...

Homework Statement Find the moment of inertia, Iy, about the y-axis using a vertical strip, width dx. Use the given equation and eliminate constants k and c, express answer in terms of number and powers of a and b. Homework Equations I can't figure out how to eliminate the constants...

I took a picture of the question to help. I know that the moment of inertia for a rod (at one end, not the center) is: 1/3ML^2 And I know that the period of oscillation is: T=2∏√(L/g) But I don't know how to relate them... I tried doing Torque=Iα=Fdcosθ and solve in terms of...

Basically, for a standard flywheel (heavy Metal disc), Is its moment of inertia a fixed internal quantity for that flywheel which doesn't change dependent on angular velocity etc?

Hello everyone! Here is the link to the problem: http://i.imgur.com/2HNrQ.jpg I don't even know where to start. Any help to get started would be greatly appreciated. Thank you so much. Cheers

Can someone please explain to me what moment of inertia means?? I googled it and I found that moment of inertia is an objects resistance to angular momentum? What does that mean exactly? Can someone please briefly explain to me (in English) what it means or give me an example? Because I really...

Homework Statement This isn't homework but its part of my assignment. I am creating a center of gravity calculator for a car using excel which I can enter the locations of different components and their masses, and it will give me the center of gravity for the car. I am then using this to...

Hello everyone, I have been working on a problem and I am having a hard time figuring out if this is the right answer. Homework Statement A solid sphere of mass 10 kg and radius 10 cm is rotating about its axis. A. Find its moment of inertia B. What is the kinetic energy of the sphere if it...

Homework Statement I'm trying to settle an argument about front wheel drive vehicles and acceleration vs inertia and traction. Homework Equations My position is that the faster a FWD car accelerates, the more inertia causes weight transfer off of the front wheels, and onto the rear wheels...

A) A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the side with length b. Express your answer in terms of given...

Homework Statement So the problem starts out like this Stick of the Gods! You hold one end of a stick, but it has no other end. It simply extends into infinity. Its one-dimensional density distribution is given by: λ=(λinitial)times(e^(-x/L)) λ is the density The problem doesn't state what...

I was working out a conceptual question that asks: if a disk and a hoop of equal mass and radius start from the top of a ramp, are realeased at the same time, and roll without slipping, which one reaches the bottom of the ramp first? Disk: I = 1/2(m)(r^2) Hoop: I = mr^2 So the inertia...

A wheel of radius 0.20 m is mounted on a frictionless horizontal axis. A massless cord wrapped around the wheel is attaches to a 2.0 kg block that slides on a horizontal frictionless surface inclined at angle θ = 20 degrees with the horizontal. The box accelerates down the surface at 2.0...

Homework Statement I am trying to find the moment of inertia of a disc (let the mass be m and radius R) inclined at an angle θ to the vertical axis. (See attachment 1) Homework Equations The Attempt at a Solution I started by taking a small element of area dA. (see attachment 2) The mass of...

Homework Statement A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. (Consider up and to the right to be the positive...

What is the differece between the two formulas numbered 3 and 6 in the paint document? And what types of questions would I use eq. 3 and eq. 6?

Homework Statement In a particular coordinate frame, the moment of inertia tensor of a rigid body is given by I = {{3,40},{4,9,0},{0,0,12}} in some units. The instantaneous angular velocity is given by ω = (2,3,4) in some units. Find a rotation matrix a that transforms to a new coordinate...

A uniform disk(I=.5mr^2), hoop(I=mr^2), and sphere(I=.4mr^2), all with the same mass and radius, can freely rotate about an axis through the center of mass (CM) of each. A massless string sis wrapped around each item. The string is used to apply a constant and equal tangential force to each...

What is "moment of inertia?" Just curious and I use it a lot but I am not entirely sure what it is. Call me an idiot but I need to know before my physics endeavors proceed.

This just struck me and I was curious.

Homework Statement Four point masses form a rigid body (they are connected by massless rigid rods) given the positions M1= 3kg (2m, 4m, 0m) M2= 2kg (1m, -4m, 0m) M3= 1kg (10m, 2m, 0m) M4= 5kg (-5m, 2m, 0m) Find: A) Moment of inertia of this system when it rotates about x axis B) Moment of...

Homework Statement The total length of the composite body is 4.5 feet. Before the propellant is burned, the projectile weighs 23 lbf. After the propellant burns, the remaining projectile weighs 16 lbf. Before the propellant is burned, the mass center is located 2.6 feet from the projectile...

Hello how can I find the moment of inertia of a circular sector about the X axis , which the sector is symmetrical about , with -θ down and θ above ?! I_{x} = ∫y^{2} dA = ∫y^{2} *y *dx Or =∫∫ y^{2} dy dx I don't know how to put the limits of integration , I turned it to polar...

I'm getting desperate. The professor has assigned a project and has not clearly explained how to derive the answers. I'm doing the best I can but his TA's and recommended tutors for the class are always incapable of reproducing the answers either. It's a junior level dynamics class, but he's...

What are they? I have some poeple telling me that for a cylinder it's I = (1/4)MR2 + (1/12)ML2 and that for a disk it's the same. Other people have told me that it's I = (1/2)MR2 for a disk and that it's the same for a cylinder. In the past I've used the former and have gotten the right answers...

Homework Statement A uniform beam of mass m = 0.6 kg and length L = 0.3 m can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F1 = 1.5 N, F2 = 1.5 N, F3 = 1.5 N and F4 = 1.5 N. F2 acts a distance d = 0.12 m from the center of...

Homework Statement When calculating moment of inertia of a disk there is something that really bothers me. I've googled this a lot and everywhere i look they 'assume' that the Δa = Δr*2∏r, formula for rectangle, not circle: (area of circle r+Δr - area of circle r) Δa = ∏(r+Δr)^2 - ∏r^2 = ∏r^2 +...

Homework Statement A closed cylindrical tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tube is rotated about a perpendicular bisector, the moment of inertia of water about the axis a)increases b)decreases c)remains constant d)increases if the...

Homework Statement A thin, cylindrical rod = 27.0 cm long with a mass m = 1.20 kg has a ball of diameter d = 10.00 cm and mass M = 2.00 kg attached to one end. The arrangement is originally vertical and stationary, with the ball at the top as shown in the figure below. The combination is...

Homework Statement Two solid spheres -- a large, massive sphere and a small sphere with low mass -- are rolled down a hill. Which one reaches the bottom of the hill first? Homework Equations ICM= (2/5)MR2 The Attempt at a Solution I thought that this would be the smaller sphere...

Homework Statement Suppose you are designing a car for a coasting race -- the cars in this race have no engines, they simply coast down a hill. Do you want large wheels or small wheels? Do you want solid, disk-like wheels, or hoop-like wheels? Should be wheels be heavy or light? (Select all...

Homework Statement Homework Equations I_a = I_G + md^2The Attempt at a Solution I tried using the parallel axis theorem to find the moment of inertia about the axis. In the formula sheet they give the moment of inertia of a hemisphere: I_G = 0.259mr^2, where d, the distance from the center is...