Moment of inertia Definition and 1000 Threads

Show by integration that the moment of inertia of the plate about an axis that is perpendicular to the plate and passes through one corner is \frac{1}{3}m(a^{2}+b^{2}) I'm not sure at all how to approach this problem. I know that the moment of inertia is \int r^{2}dm but how do I use that in...

Homework Statement I need to find the Moment of Inertia of semicircular disc to do some question. I have done these kind of questions before (Long time ago:shy:) but for some reason i can't recall how, and even when i moved to my new home, i lost my notes :cry: Please can someone put...

Homework Statement How do you derive the moment of inertia for a hollow sphere? I am not ending up with what i need to get which is: (8pir^5)/9 Homework Equations I am not sure if the bounds are correct or if we need to factor something else in. The Attempt at a Solution A double integral...

Homework Statement A slab has width a, length a, and thickness a/4. What is the moment of inertia about its symmetry axis? Use the one parallel to the large face of the slab. Homework Equations The Attempt at a Solution The answer is supposedly (ma2)/12 + m(a/4)2/12. I can't...

Homework Statement A disc shaped object is made of a non-uniform material. Its radius is r and it is fre to rotate about an axis through its centre. If a force F applied tangentially at the edge of the object produces the angular acceleration a, what is its moment of inertia for rotation...

So, we learned that the units of Moment of Inertia are mm^4. My question is how do they use moment of inertia in static calculation (where we use Newtons), if Moment of Inertia is in mm^4?

Homework Statement Find the moment of inertia of a cube, all edges length A, with mass M through the centre ( through mid point of 2 opposite sides) Homework Equations I = integral( r^2 dm dm = density x volume where volume of a slice ( thin) square = AxAxdx = A^2 dx = p A^2...

Homework Statement The moment of inertia (in4) about the y-axis is most nearly (a) 39,500 (b) 37,600 (c) 38,700 (d) 36,400 Homework Equations Iy(circle)= .25(pi)(r^4) Iy(triangle)= (1/12)h(b^3) parralel axis theorem= Iy=Iy'+A[d(x)]^2 The Attempt at a Solution Iy(circle)=...

I think i have this right, but would like to confirm i did the right thing: Homework Statement I have a lamina disc radius R with a disc of radius r cut out of it from its centre. Total mass of the actual object is M, Find moment of inertia when lamina rotates about axis perpendicular to...

Homework Statement Two rocks, with masses m1 and m2, are attached to the opposite ends of a rope that runs around the inner radius r of a pulley with moment of inertia I m1 = 10 kg m2 = 50kg I = 60 kg*m^2 r = 1 m I have to determine Tension for both masses and the angular...

It must be for any value of the distances (work with letters only), Every distance is known, mass is also known I just can't figure out how to do it if anyone can help me I would really apreciate it. Take also in consideration that we must use point E as the reference Here is the image, in...

Homework Statement Find the shape of the solid of revolution with the minimum moment of inertia about it's axis, given the volume is fixed. Homework Equations I=\int\frac{1}{2}r^2dm=\int\frac{1}{2}r^2\rho~dV=\int\frac{\rho\pi}{2}r^4dz V=\int \pir^2dz I+\lambda V must be stationary. The...

Homework Statement A thin rod has mass M and length L. What is the moment of inertia tensor about the center of mass if placed along the x axis. Homework Equations I would write the inertia tensor in component notation, but I don't know how to use Latex. The Attempt at a Solution...

I need help solving a mass moment of inertia for a slider crank mechanism. I've done my best to sketch it in the attachment. This will be used for sizing of a motor. Homework Statement Link A has mass Ma and is located Acg distance from its pivot point Z Link B has mass Mb and is located Bcg...

Hey I'm making some kind of simulation... (in game maker) Ball collisions, ball to wall(friction)etc. So I'm asking: how do i calculate rotational speed if i know r, mass, and distance to where is force being applyed? I know that moment of inertia for a ball is 2/3*m*r2 and have no idea...

There is nothing to answer anymore. I have no time left for the project to use the data.

See the attached PDF document, all information is given and the help I need is on number 2-5, which is all one problem. I do already know that you have to do 2, then 5, then 3, then 4. Between 30 of my friends and I, we cannot get it. Thanks in advance.

Homework Statement We have 3 discs, arranged as the sketch below shows. Find the moment of inertia of the whole system around the axis, passing horizontally through center of the bigger disk: 1. Two smaller disks are fixed and cannot rotate around their axes. 2. Two smaller disks can...

Homework Statement Estimate the total rotational moment of inertia in Kg*m^2, of all the motors and generators in the Eastern United States. Homework Equations No other information was provided. The Attempt at a Solution First off I went to the following website to estimate the...

hello, I need help finding the moment of inertia of a cone using triple integral. can you also explain how can we get dV with details?

IPS drives me nuts. If I know an object's weight in lbf (a flat, 10" radius disk for simplicity's sake), and want to find it's MOI, the formula is I = 1/2*w/g*r2. Now here's where i get confused: Since I have the object's weight in lbf, it's mass is numerically equal, so a weight of 2.6lbf...

Hi all. It's been a while since I've taken mechanics of solids, I was hoping I could get some confusion ironed out here. I have a long thin plate with C channels welded along its length, below is a cross sectional view. [PLAIN]http://img375.imageshack.us/img375/6672/channelexcel.jpg As you...

Homework Statement Two masses, having mass moments of inertia J1 and J2, are placed on rotating rigid shafts that are connected by gears. If the numbers of teeth on gears 1 and 2 are n1 and n2, respectively, find the equivalent mass moment of inertia corresponding to theta_1. Homework...

Hi, I am working through the Feynman lectures on physics and trying to calculate the moment of inertia stated in the title. (the taxis of rotation going through c.m., orthogonal to length). My approach is to slice the cylinder into thin rods along the length, using the parallel taxis theorem...

I have a question but got two different answers by two different methods. The question: "Two workers are holding an 80kg plank, one worker let's go. The weight is carried by 55% of the first worker. It is 2.5m long and no uniform. The angular acceleration is 5.5 rads/s^2, what is the moment of...

Homework Statement A hollow cylinder has mass m, and outside radius r_{2}, and an inside radius r_{1}. Use intergration to show that the moment of inertia about its axis is give by I=\frac{1}{2}m(r^2_2+r_1^2). Uniform composition is assumed. Homework Equations I=\int r^2dm dm=\sigma dA and...

Homework Statement Homework Equations I=p\int_{0}^{0.85}r^2dV where p is density and r is perpendicular distance from the axis of rotation. dV=dxdydz The Attempt at a Solution I'm not sure where I'm going with this one as it seems I'll have to integrate dx*dy*dz which is kind of confusing...

Homework Statement Calculate the moment of inertia for the following beam cross-section http://www.freeimagehosting.net/uploads/th.044a09fe2e.png The center (lighter) area is hollow down the length of the beam. The centroid is marked. The wall thickness is 1/4" and the dimension of...

I am trying to create a model in SimMechanics of a simple damped frame. I am very new to this software and structural dynamics as well. I have a copy of "Dynamics of Structures" 3ed by Chopra. In the textbook, the author uses the standard geometric and material properties that I am familiar...

Homework Statement The flywheel of an engine has a moment of inertia 2.50 (kg)m^2 about its rotation axis. What constant torque is required to bring it up to an angular speed of 400 rev/min in a time of 8.00s, starting from rest?Time (t) =8.00 sec Ang Velocity (W) = 400 rev/min Moment of...

Homework Statement If an object is not spinning, does that mean the object's moment of inertia is 0? I've always thought that it is. But is it only not spinning when the object is at the moment arm?

Homework Statement Suppose we rotate a grapefruit and a metal ring on a dining table with a smooth surface. Grapefruit has a volume of 575 cm3 and density of 0.4 g/cm3, while the ring has mass of 57 g, length of 2 cm and area of 38.5 cm2. Determine A. Moment of inertia of each of the...

our lecturer defined MI as inertia of body in circular motion(i don't know anything about inertia) except that it is something to oppose my question is that when M.I in circular motion depends on both mass and radius(distance from axis) of the body. why MI is represented as mr^2 why is it...

Homework Statement A flywheel has a moment of inertia of 0.5kgm^2, diameter 0.5m and is rotating at 1000rpm. A tangential frictional force of 1000N is applied to its rim. Calculate the time IN MINUTES for the flywheel to stop. Homework Equations None given, I assume: Torque =...

Homework Statement What is the moment of inertia WRT to the x-axis (Ix) of a right triangle with base b and height h where the legs of the triangle coincide with the x and y axis? It would be helpful to know both the single integral and double integral method. Homework Equations Ix=int(y^2 dA)...

Homework Statement An object consists of three point masses (m1=0.2 kg, m2=0.3 kg and m3=0.5 kg) attached to a massless rigid rod. The masses are located at 0 m, 0.4 m, and 0.8 m respectively. (The rod is 0.8 m in length so the 0.5 kg mass is attached to one end and the 0.2 kg mass to the...

Homework Statement Find the moment of inertia of a circular wire hoop about a point on the hoop. mass = m radius = r Homework Equations Izz = Iyy + IxxThe Attempt at a Solution Well, using the above equation I first tried to solve for Ixx. Since we are looking for the moment of inertia about a...

Homework Statement How to calculat the moment of inertia of a thin wall, the surface area of a ball of mass m and radii a. Homework Equations I=mr2 The Attempt at a Solution Spherical coordinates. dm=\frac{m}{4\pi a^2}\cdot a^2\cdot d\theta d\phi See drawing...

Hi, can anyone kindly explain to me (assuming no knowledge of spectral theorem, but only simple linear algebra understanding) how to see the vanishing of the terms Ixy, Iyz etc., where only the terms Ixx, Iyy and Izz remain? Thanks.

Homework Statement Ok So here's my question. The physical Pendulum consists of a thin rod of mass m = 100 g and length 80 cm, and a spherical bob of mass M = 500 g and radius R = 25 cm. There a pivot P at the top of the rod. (Sorry, I don't have a picture >.<) a) It asks for the center of...

Homework Statement Please help me do these : [PLAIN]http://broadcastsol.com/321.JPG Prob1 The mechanical system of massless members is shown in the figure. Determine the relationship between two forces P1 and P2 to keep the system in equilibrium at position as showing in the...

Homework Statement This is a two part problem, I answered the first but was wondering if I did the second part right. a) Consider a rigid 3-mass system (with origin at the leftmost mass 3 kg) which can rotate about an axis perpendicular to the system. The masses are separated by rods of...

Homework Statement A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolutions per 8.00s? Assume it is a solid cylinder. Homework Equations \DeltaKE=Wnet=1/2(Iw2)=14211.7J...

Homework Statement A spool of wire mass m and radius r is unwound under a constant force F. Assuming that the spool is a uniform solid cylinder that does not slip, show that the acceleration of the center of the mass is 4F/3m Homework Equations F+f=ma f=ma-F \tau =I\alpha=Fr-fr...

Homework Statement A 28.5 kg block (m1) is on a horizontal surface, connected to a 6.10 kg block (m2) by a massless string. The frictionless pulley has a s R = 0.087 m and a moment of inertia I=0.140 kgm2. A force F = 231.3 N acts on m1 at an angle theta = 30.5°. There is no friction between...

Homework Statement A solid door of mass 25.40 kg is 2.31 m high, 1.48 m wide, and 2.58 cm thick. What is the moment of inertia of the door about the axis through its hinges? Homework Equations I=(1/12)m(a^2 + b^2) + mr^2 (parallel axis theorem) The Attempt at a Solution I...

Homework Statement Find the moment of inertia of a rod with mass M, that has a mass m1, L/2 to the left of the axis of rotation and a mass m2, L/4 to the right of the axis of rotation. L is the length of the entire rod? Not sure what to do. My professor said that I had to use the parallel...

Homework Statement Calculate the moment of inertia of a spherical shell (i.e. hollow sphere) of uniform surface density about an axis passing through its center. Homework Equations The Attempt at a Solution Integral ( r^2 * dm) Integral (r^2 * p * dV) ... where p=density p * Integral (r^2 *...

A disk, cylinder shaped, of mass m and radius r is initially motionless on an ice rink. It has a massless string wound around it which you pull with a constant force F. After your hand has moved a distance d. How far has the c.m. of the disk moved? If someone could show me how I could do this...

Homework Statement Two small masses are attached to a massless rod of length 2.36 m as shown. Mass M1 is 2.53 kg and mass M2 is 5.16 kg. A) What is the distance, x, from mass M1 to the centre of mass of this system? B) What is the moment of inertia of this system about an axis that passes...