Moment of inertia Definition and 1000 Threads

  1. Fantini

    MHB Moment of Inertia of a plate with respect to one diagonal

    The problem is to show that the moment of inertia of a rectangular plate of mass $m$ and sides $2a$ and $2b$ about the diagonal is $\displaystyle \frac{2}{3} \frac{m a^2 b^2}{a^2+b^2}.$ I did it using the traditional definition of moment of inertia, that is, $$I = \int r^2 \, dm.$$ However, the...
  2. C

    How to Calculate Aircraft Pitching Moment of Inertia

    Hi everyone, I have a question which requires me to calculate aircraft pitching moment of inertia. I looked everywhere and can't find much about it, just the basis "what is inertia etc". Can anyone give an example on how to calculate pitching moment of inertia. Thanks a lot
  3. C

    What is the Moment of Inertia of a Cone about its Longitudinal Axis?

    Homework Statement Find the moment of inertia of a solid cone about its longitudinal axis (z-axis) The cone: x^2+y^2<=z^2, 0<=z<=h I_z = \int\int\int_T(x^2+y^2)dxdydzHomework Equations Representing the cone in cylindrical coords: x=zcos\theta y=zsin\theta z=z The Attempt at a Solution...
  4. M

    Moment of inertia of a rod at an angle to the axis

    suppose a uniform rod of mass M and length L is at an angle B to the x axis, one end of the the rod touching the axis. wish to find moment of inertia about x axis. let the rod touches the axis at x=0. let D=density=M/L, and I will integrate along x axis, that means that at a distance x from the...
  5. S

    Polar moment of inertia in a rod?

    How is the polar moment of inertia in a rod calculated? Thanks.
  6. S

    Polar mass moment of inertia *and* simply moment of inertia

    Hi ,everyone… i wanted to clear my one confusion ,that what is actual difference between polar mass moment of inertia and simply moment of inertia…??
  7. P

    Acceleration, Uniform Ball on Incline

    Homework Statement [/B] A uniform solid ball of mass m rolls without slipping down a right angled wedge of mass M and angle θ from the horizontal, which itself can slide without friction on a horizontal floor. Find the acceleration of the ball relative to the wedge. 2. The attempt at a...
  8. T

    Calculating the moment of inertia of a filled cylinder

    Homework Statement For my IB higher level physics extended essay I will have to calculate the angular momentum of a cylinder rolling down a slope. The cylinder is made out of copper and will be filled with a known mass of car engine oil. I think i can obtain the angular velocity fairly easily...
  9. T

    Tensor moment of inertia -- why is there a "-" sign?

    why there is a negative sign in the tensor moment of inertia??
  10. gracy

    Moment of Inertia: Ignoring Small Bond Axis Molecule

    Why the moment of inertia of a molecule about the bond axis is small enough to ignore ?
  11. 462chevelle

    Moment of Inertia power plant energy

    Homework Statement It has been suggested that we should use our power plants to generate energy in the off-hours (such as late at night) and store it for use during the day. One idea put forward is to store the energy in large flywheels. Suppose we want to build such a flywheel in the shape of...
  12. R

    What is the correct way to find the inertia of a bullet entering a door?

    I am having trouble with this one problem. I have tried multiple times to solve it, but come up with the same wrong answer every time. The mistake that I may be making is in finding the Inertia of the bullet entering the door: I figured that some mass at the given radius from the hinge of the...
  13. S

    Tipping cylinder tube with balls in it

    Problem Statement Two identical spheres of radius r are placed inside a cylinder of radius R as shown in the diagram below. You are given that R/2 < r < R and that each ball has a weight W. All surfaces are smooth. Show that there is a minimum mass, m, of the cylinder which will allow it to...
  14. R

    Moment of Inertia - center of a rod w/ unequal distribution

    Hello everyone! New member here, as an ME major I always seem to come across very valuable information here, so I figured I would see if possibly someone here could help me. The problem I am dealing with involves modeling a car through certain motions such as hitting a speed bump, and part...
  15. andyrk

    Why Can't Moment of Inertia Exceed MR² for Solid Bodies?

    How do we know that moment of inertia cannot exceed MR2 for a solid body like solid cylinder, solid sphere, hollow sphere etc? R is the radius of the object in consideration. I know it has something to do with- that for solid bodies (in some cases hollow also) there are a lot of point masses in...
  16. A

    Torque v. Time Graph -- Find angular velocity

    Homework Statement An object whose moment of inertia is 3.00kgm2experiences the torque shown in the figure (Figure 1) . What is the object's angular velocity at 2.80s ? Assume it starts from rest. http://session.masteringphysics.com/problemAsset/1073771/4/knight_Figure_13_21.jpg Homework...
  17. E

    Finding Rotational Speed once the Moment of Inertia Increase

    Homework Statement A trapeze artist performs an aerial maneuver. While in a tucked position, as shown in Figure A, she rotates about her center of mass at a rate of 6.03 rad/s. Her moment of inertia about this axis is 16.1 kg·m2. A short time later the aerialist is in the straight position, as...
  18. T

    How Do You Calculate the Moment of Inertia for a Door?

    Homework Statement A uniform, thin, solid door has height 2.2 m, width .87m and mass 23kg. Find the moment of inertia for rotation on its hinges. 2. Homework Equations I=∫x^2dm The Attempt at a Solution [/B]The way I set it up was that I made into strips of length H (height) and width dr...
  19. R

    Moment of Inertia about the CoM

    Homework Statement A puck of mass 82.0g and radius 4.09cm slides along an air table at a speed of v = 1.59m/s. It makes a glancing collision with a second puck of radius 6.97cm and mass 130g (initially at rest) such that their rims just touch. The pucks stick together and spin after the...
  20. L

    Non-Uniform Gear Moment of Inertia

    I'm working on a project involving analyzing the motion of a reciprocating saw. This saw converts rotational motion from an electric motor to linear motion by means of a slider crank mechanism. The power transmission goes from motor and attached driving gear, to crank, to connecting rod, to...
  21. Crush1986

    Moment of Inertia Compass Needle

    Homework Statement You place a magnetic compass on a horizontal surface, allow the needle to settle, and then give the compass a gentle wiggle to cause the needle to oscillate about its equilibrium position. The oscillation frequency is 0.321 Hz. Earth's magnetic field at the location of the...
  22. S

    Moment of inertia and angular velocity of a uniform disk

    Homework Statement Two particles, each of mass m, are attached one to each end of a diameter PQ of a uniform circular disk, of mass 4m, radius a with its centre at O. The system is free to rotate about a horizontal axis through A, a point on PQ such that OA = b as indicated in the diagram...
  23. Q

    Moment of Inertia of a rod and two spheres

    Homework Statement A barbell that consist of a long thin rod of mass M and length L is attached to two uniform spheres on each end. Both spheres have mass M and (1/3)L. The sphere on the left is hallow (spherical shell) and the sphere on the right is solid. What is the moment of inertia for...
  24. C

    How to Graph Moment of Inertia and Frictional Torque?

    Homework Statement The moment of inertia (I) of the bicycle wheel about the axle, can be obtained graphically using the equation: rm(g-a) = I(a/r)+Frictional Torque. Explain how to form two variables so that, I and Frictional Torque can be obtained from a linear graph. Identify the constants...
  25. S

    Lagrangian mechanics: sphere inside a cylinder

    The problem goes by this: A sphere of radius ##\rho## is constrained to roll without slipping on the lower half of the inner surface of a hollow cylinder of inside radius R. Determine the Lagrangian function, the equation of constraint, and Lagrange's equations of motion. Find the frequency of...
  26. D

    Calculate the moment of inertia for the system

    Homework Statement Calculate the moment of inertia for the system. The rods of length L are massless. Image here: http://imgur.com/O639ejf Homework Equations /answer[/B] I know that I=ΣMR^2 The correct answer to the problem is 32ml^2 I JUST WOULD LIKE TO SEE HOW THE PROBLEM IS DONE...
  27. L

    The moment of inertia of a rod that is rotating off the end of the rod.

    Is there a formula for the moment of inertia? A thin, uniform density rod is rotating about an axis that is off the end of the rod, so it looks a bit like this: ------- | (------- is the rod and | is the axis of rotation, so the rod is rotating out of the plane of your screen) I just have...
  28. S

    Proof of disk moment of inertia using area density

    Homework Statement Disk with radius R σ = M/A I = ∫ mr2 Homework Equations Today we learned how to derive various moments of inertia via density equations (M/L, M/A, M/V). I understand all of them except on how to get MR2/2 for a disk. The Attempt at a Solution I = ∫mr2 σ = M/A dM =...
  29. M

    A spinning space station exhibits a change in moment of inertia.

    Homework Statement A space station shaped like a giant wheel has a radius 95.0 m and a moment of inertia of 5.03✕ 108 kg · m2. A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1g. When 100 people move to the center of the...
  30. C

    Moment of Inertia of a solid sphere

    Homework Statement Taylor, Classical Mechanics Problem 10.11 ** a) Use the result of problem 10.4 (derivation of the general integral for a moment of inertia of a continuous mass distribution in spherical coordinates, using point particles) to find the moment of inertia of a uniform solid...
  31. Aristotle

    Question relevant to Moments of Inertia

    Homework Statement Homework Equations I= ∑ miri^2 ? The Attempt at a Solution I'm not sure on how to start this problem. How exactly do I know which one is IA, IB, IC since it didnt specify? Can somebody please hint me in solving this problem?
  32. K

    Complex Moment of Inertia Calculation

    Homework Statement I'm just looking for the proper equation to use to find the moment of inertia of a complex assembly of bodies. I'm not a student and this isn't homework, but it seemed the most relevant place to pose the question. One of my hobbies is making toys and I'm trying to calculate...
  33. T

    Unequal tension of a rope in a pulley system

    I am having a bit of difficulty with the concept of unequal tension in a rope. What are the conditions for unequal tension? I read that the tension is the same when there is no acceleration. Why is this the case? Can someone explain this concept to me? Thanks :)
  34. M

    Calculating moment of inertia for nonuniform sphere

    Homework Statement A sphere with radius R = 0.200 m has density ρ that decreases with distance r from the center of the sphere according to \rho = 3.00 \times 10^3 \frac{kg}{m^3} - (9.00 \times 10^3 \frac{kg}{m^4})r a) Calculate the total mass of the sphere. b) Calculate the moment of inertia...
  35. N

    Moment of Inertia, working backwards

    I've to work out b & d in this equasion. I=bd^3/12 I know that the ratio between b & d in this case is 1.166 and I am given the value of I. It is an engineering problem as the software will only allow the use of square/rectangular or round section but we are using H section and we are allowed...
  36. P

    Moment of inertia about a ceiling fan?

    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...
  37. Hardik Batra

    How is the moment of inertia related to the square of the distance?

    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.?
  38. M

    How Fast Must a Bullet Travel to Tip a Rotating Cube?

    Homework Statement 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. Find the...
  39. N

    Moment Of Inertia Of a Weld Profile

    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...
  40. Lord Crc

    Rigid body, torque and moment of inertia

    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...
  41. J

    Moment of inertia ice skater problem

    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...
  42. S

    Why Is the Mass of a Wheel Concentrated on the Rim?

    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 !
  43. B

    Moment of Inertia of Hollow Cylinder Derivation

    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...
  44. B

    Moment of inertia and torque problem

    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...
  45. deep838

    Is the Moment of Inertia strictly different

    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.
  46. stateofdogma

    Moment of inertia of rectangle without dd int

    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...
  47. B

    Moment of Inertia for Half Disk

    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...
  48. J

    Composite moment of inertia question:

    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...
  49. K

    Differential moment of inertia

    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) =...
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