Inertia Definition and 1000 Threads

Inertia is the resistance of any physical object to any change in its velocity. This includes changes to the object's speed, or direction of motion.
An aspect of this property is the tendency of objects to keep moving in a straight line at a constant speed, when no forces act upon them.
Inertia comes from the Latin word, iners, meaning idle, sluggish. Inertia is one of the primary manifestations of mass, which is a quantitative property of physical systems. Isaac Newton defined inertia as his first law in his Philosophiæ Naturalis Principia Mathematica, which states:

The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.
In common usage, the term "inertia" may refer to an object's "amount of resistance to change in velocity" or for simpler terms, "resistance to a change in motion" (which is quantified by its mass), or sometimes to its momentum, depending on the context. The term "inertia" is more properly understood as shorthand for "the principle of inertia" as described by Newton in his first law of motion: an object not subject to any net external force moves at a constant velocity. Thus, an object will continue moving at its current velocity until some force causes its speed or direction to change.
On the surface of the Earth, inertia is often masked by gravity and the effects of friction and air resistance, both of which tend to decrease the speed of moving objects (commonly to the point of rest). This misled the philosopher Aristotle to believe that objects would move only as long as force was applied to them.The principle of inertia is one of the fundamental principles in classical physics that are still used today to describe the motion of objects and how they are affected by the applied forces on them.

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  1. avito009

    Does the Moment of Inertia Change with Position?

    I had a discussion with my friend. He took an icecream stick and told me that if the stick was held horizontally the stick would break easily but if you held the stick vertically it would be difficult to break the stick. He said that vertically the moment of inertia is more. My question is that...
  2. K

    Moment of Inertia of an L-shaped bar

    Homework Statement The L-shaped bar of mass m is lying on the horizontal surface when the force P is applied at A as shown. Determine the initial acceleration of point A. Neglect friction and the thickness of the bar. (Sorry, don´t know how to get you a better picture) L...
  3. W

    Decomposing angular velocity and moment of inertia

    Homework Statement See the attached image. Homework Equations ##T = 1/2 \omega^2 I## The Attempt at a Solution So ##I_1,I_2,I_3## are just the moments of inertia of the object with regards to the 3 axes. Right? OK, then I intuitively assume that the total kinetic energy must simply be...
  4. S

    How Do You Calculate the Mass of a Rotating Square Plate?

    Homework Statement A square plate has a side length of 1.2 m. An applied torque of 300 N · m gives the plate an angular acceleration of 4.8 rad/s2 about an axis through the centre of the plate. Determine the plate’s mass. Homework Equations t = lα l = 1/12M(l^2 + w^2) The Attempt at a...
  5. X

    Rotational inertia of a rod that has mass on one end

    Homework Statement a 3 kg mass is on the end of a metal rod which is pivoted at one end. the mass of the rod is 2kg its length is 4 meters Homework Equations I=(ML^2)/3 The Attempt at a Solution the rotational inertia of the rod itself is 10.6 but i don't know how the 3kg mass at the end...
  6. T

    Moment of Inertia for Composite Object

    Homework Statement for this composite object, what moment of inertia needs to be used if you were to sum the moments about the centroid of the object, \sum M=I\ddot\theta Homework EquationsThe Attempt at a Solution is it the sum of the I_zfor a solid sphere and a solid cylinder
  7. Spock

    Can centripetal/centrifugal force raise itself

    So my question is, if a laithwaite engine (my attached photo) spins fast enough, will it be able to lift off the ground? And if yes, what's the maths to calculate the speed needed to make it lift?
  8. O

    Understanding Moment of Inertia in a Ball-Rod System

    Homework Statement "a uniform steel rod of length 1.20 meters and mass 6.40 kg has attached to each end a small ball of mass 1.06 kg. The rod is constrained to rotate in a horizontal plane about a vertical axis through its midpoint. Find the moment of inertia of the ball-rod system." Homework...
  9. P

    Moment of Inertia of a Regular Hexagon

    A equilateral triangular lamina, has a moment of Inertia of I if the axis of rotation passes through the centroid of the triangle, perpendicular to it's plane. What is the moment of inertia of a regular hexagon(Again, through it's geometrical centre, perpendicular to the plane), provided that...
  10. M

    Center of gravity/moment of inertia

    I am doing a mini hovercraft project. Regarding my design, I plan to place the fan (LIFT) in the middle of a rectangular styrofoam board (15 inches by 8inches). The position of my fan would be (x=7.5, y=4in); this would also be my center of gravity. My origin (coordinate) is at the corner of...
  11. Q

    Rotational EOM's with non diagonal inertia tensor

    I'm having difficulties understanding how I should calculate the angular velocities of a rigid body when the inertia tensor is given in body coordinates and has off diagonal elements. Let's assume I have an inertia tensor ## I = \begin{bmatrix} I_{xx} & -I_{xy} & -I_{xz} \\ -I_{yx} &...
  12. S

    Moments of Inertia Explained: Helping Scott Understand Statics

    Hey there, In my statics class we're just finishing up moments of area or moments of inertia as they're being called. I can do the math and figure them out just fine but I have no clue what I'm actually finding! What is it? I am having trouble actually conceptualizing what it is that I'm...
  13. K

    How to calculate equivalent inertia of an engine?

    Hello, is there a formula or technique to calculate the equivalent inertia of an engine? I think I will have to add up all the inertias of everything else rotating inside it but it has so many components like cams, followers, pulleys, water pump, crank, flywheel etc. What sort of effect will...
  14. S

    Experimental value for moment of inertia - Not about c.o.m.

    Homework Statement These are the pre lab tasks for my upcoming lab. Find the theoretical value for moment of inertia for a ring with off axis rotation using parallel axis theorem and outline procedure to obtain experimental value of I. During the lab we will be using a rotating platter with a...
  15. L

    Apply impulse to a wheel creates constant acceleration?

    Hello! Well, I am in trouble with this question for some time. I am making a simulator with autonomous cars and its movement is done applying constant impulses to the wheel. My question is: if the vehicle is in the intertia state and I start to apply this impulses, the vehicle will assume a...
  16. H

    What is the role of moment of inertia in rotational motion?

    I've been studying rotational motion for a while and I have no clue how moment of inertia plays a role in it. How would you define it? Often times, it's just described as resistance to change. Does that mean a high moment of inertia means a higher resistance to change or is it the other way...
  17. A

    Moment of inertia in plane translation

    I have a doubt in my mind regarding moment of inertia.in my textbook a question is somewhat like this The center of a disc of mass 'M' and radius 'R' is at a distance 'd' (here 'd' >'R') from a certain point 'O'.what is the moment of inertia of the disc about an axis perpendicular to the plane...
  18. C

    Moment of Inertia of 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 = 2.9 kg and radius R = 0.22 m. The rods each have mass mr = 1.4 kg and length L = 0.83 m. 1) What is the moment of inertia of each rod about the axis of rotation...
  19. R

    Moment of inertia of half disk through integration

    Hello, sorry for this stupid question. I struggled to find the moment of inertia of half solid thin disk (about the center of the disk) through an integration, but I couldn't get the right value. I'm pretty sure it has to be MR^2/4, but I=\int r^2 dm \\ dm=(M/A)dS With A=\pi R^2/2 I compute...
  20. D

    Eigenvectors of Inertia tensor

    Hi, I've written a little fortran code that computes the three Eigenvectors \vec{v}_1, \vec{v}_2, \vec{v}_3 of the inertia tensor of a N-Particle system. Now I observed something that I cannot explain analytically: Assume the position vector \vec{r}_i of each particle to be given with respect...
  21. W

    Area/2nd Moment of Inertia of an arc/ring

    Homework Statement I'm trying to solve for the area moment of inertia of a curved arc. To visualize this, it would be like a bent piece of cardboard (two arcs with two lines connecting them at their end points). I'm modelling the differences in area MOI with an increasingly curved piece of...
  22. E

    Moment of Inertia of 4 Balls on Square Side

    Homework Statement There are four solid balls with their centres at the four corners of a square of side a. The mass of each sphere is m and radius is r. Find the moment of inertia of the system about one of the sides of the square. Homework EquationsThe Attempt at a Solution I= 2 (two balls)...
  23. JesseJC

    Moment of Inertia about an axis at the center of mass

    Homework Statement 3.) What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)...
  24. A

    Find the moment of inertia of the system

    Two rectangular objects, each 1.0 m by 3.0 m, are attached as shown. Each rectangle has a mass of 1.5 kg. Find the moment of inertia of the system about (a) axis A, (b) axis B, and (c) axis C. I have no idea what to do, any help is appreciated.
  25. P

    Can liquids be treated as rigid bodies for moment of inertia

    Consider a partially filled bottle of water. When it's tipped over and rotating about its pivot point where its edge touches the ground, it has an angular acceleration. Assuming the liquid is not viscous at all, so flows perfectly, at a given instant can it be considered to have a moment of...
  26. K

    Two masses hanging from a pulley (conservation of energy)

    Homework Statement Two masses are connected by a string that hangs over a frictionless pulley with mass 8kg, radius .25m, and moment of inertia .5mr^2. One mass lays on the ground and has mass 15kg. The other mass is 22.5 kg and is 2.75 m above the ground. Use conservation of energy to...
  27. B

    How to Solve Moment of Inertia for a Cylinder with Varying Radii?

    Homework Statement So I generally understand how to solve the following problem. My only roadblock is that I am not sure I am solving the moment of Inertia correctly. I know that for a solid cylinder you would use I = 1/2mr^2, but I am not sure how if it has only one mass given of 10 kg, yet...
  28. avito009

    Is Friction the Reason Spinning Tops Eventually Stop Rotating?

    As per Newton an object that is rotating at constant angular velocity will remain rotating unless it is acted upon by an external torque. But we know that a top will stop rotating after some time. So does that mean that the external torque is the friction of the floor on which the top rotates?
  29. Y

    Moment of inertia and rotational motion

    Hello, I am currently attempting to cover rotational motion using Halliday's Fundamentals of Physics. I understand very well the concept of moment of inertia as defined as the sum Σmi*ri2. However, the textbook argues that if there are too many particles, the moment of inertia can be defined as...
  30. avito009

    Moment of Inertia at a point away from centre of Mass.

    Lets say we are sitting on a horse at the edge of a merry-go-round. You move faster relative to a point near the centre of the merry go round. Now most of the mass of this merry go round is at the edge i.e at the horse. So the moment of inertia at the horse is less. Correct me if I am wrong.
  31. aladinlamp

    How Much Energy Can Be Extracted from a Rotating Disk?

    As you can see, solid disk is rotating at steady angular speed, without any external force beeing applied. If i stop it gradualy within 60 second, by applying some linear load, how many kWh can i extract from this moving object?
  32. S

    How do I calculate moment of inertia in a wheel?

    What I have are two wheels, weight assumed at 50 kg overall for both, joined by an axle. The wheels are 900 mm apart from the centre of one tire to the centre of the other. The diameter of the tire is 690 mm. How do I calculate the moment of inertia in order to find the torque in the centre of...
  33. L

    Inertia and a Rocket that doesn't accelerate anymore

    Let's say we are on Earth-like planet, but without an athmosphere. There's a rocket on the ground and it's starting now. The rocket accelerates but at a point when it has enough speed it stops accelerating. The rocket has still enough speed to get further away from the planet but not enough to...
  34. DocZaius

    Moment of Inertia of a Square: Problem with Certain Method

    For fun, I thought I would try to derive the moment of inertia of a square using different approaches (in each case, changing the differential area being integrated). Everything went well until I tried the approach of first considering the disk in the center of the square, then adding the bits...
  35. Science2Dmax

    Is it possible for antimatter to different inertia?

    If inertia is a property of matter, does this mean that antimatter has some sort of different inertia? Again, haven't taken a physics class science I'm only in junior high. Please don't judge me
  36. H

    Moment of inertia of a solid sphere

    Homework Statement Find the moment of inertia of a solid sphere of uniform mass density (like a billiard ball) about an axis through its center Homework Equations I = ∫rρdV The Attempt at a Solution I =ρ ∫r4πr2dr = ρ4π∫r4 Then I integrate this from 0 (the center) to R, so I = (ρ4π)*(R5/5) And...
  37. PrincessIceFall

    What is the mass moment of inertia?

    What is the mass moment of inertia about the longitudinal axis of the shape attached in this thread, but in 3 D? I found this "Handbook of Equation for Mass and Area Properties of Various Geometrical Shapes" which gives the mass moment of inertia of a regular octagon. I initially thought that...
  38. P

    How Do You Calculate Moment of Inertia for CD and FE in a Multi-Rod System?

    If we have five identical rigid rods, each of length l and mass m, are connected together to form the system shown in the figure. The system may rotate about an axis passing through AB. The question is to find the moment of inertia of the system with respect to axis AB. I managed to find the...
  39. M

    Finding mass from moment of inertia graph - inconsistency?

    Homework Statement I have a disk that can rotate about an axis at a radial distance h from the center of the disk. I am given a graph showing the the rotational inertia I of the disk as a function of the distance h from the center of the disk out to the edge of the disk. From the graph (see...
  40. Alettix

    Determination of moment of inertia of a hollow cylinder

    Hi! I got the task to determine the moment of inertia of a hollow cylinder, however it's not about just measuring the mass and the inner and outer radius and putting it into the right formula, instead I should roll it down an inclined plane. 1. Homework Statement I'm only allowed to use the...
  41. B

    Moment Of Inertia Of Non-uniform Rod

    Hello, I am trying to find the moment of inertia of a uniform rod, that has a mass added to it at some position along it's length, which is equal to the mass of the rod itself, and the axis of rotation is at one end. 1. Homework Statement A uniform, \mathrm{1.00m} stick hangs from a...
  42. A

    How Do Collisions Affect the Moment of Inertia and Angular Momentum of a Rod?

    I am trying to learn to calculate collisions on the center of percussion of a rod. Can you tell me how to find the moment of inertia? Suppose we have a rod of length 1m and mass M = 12 kg., we know that ##I = 12 * 1^2 / 3 = 4## , if a collision takes place at the CoP ( at 0.166666 m from the...
  43. D

    Find moment of inertia via torque and acceleration parameter

    Homework Statement 2-1. A constant torque of 4 Nm is applied to an unloaded motor at rest at time t = 0. The motor reaches a speed of 1717 rpm in 4 s. Assuming the damping to be negligible, calculate the motor inertia in Nm·s2. Homework Equations T = J(eff) * dw/dt J = kg*M^2 The Attempt at a...
  44. lovethepirk

    Understanding moment of inertia values

    I have done some extensive self study on MOI but I don't understand it's meaning in application. An example is imagine a stick of butter is dropped on the ground. Now ignoring friction and the other variables we can remove for learning purposes, let's assume the butter stick is kicked and it...
  45. M

    Why is mass dependent on inertia and not vice versa?

    in here: http://www.physicsclassroom.com/class/newtlaws/Lesson-1/Inertia-and-Mass Mass as a Measure of the Amount of Inertia All objects resist changes in their state of motion. All objects have this tendency - they have inertia. But do some objects have more of a tendency to resist changes...
  46. G

    What's the distance a sphere travels from inclined plane?

    < Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > So the problem that I have been assigned has formulas of rotational energy, momentum, trajectories, inertia, and inclined planes. A solid sphere is rolling down an inclined plane (that is placed...
  47. Shaheen Uqab

    Calculate moment of inertia of a "L" angle bent in a parabola

    I want to calculate moment of inertia of an angle L bent in form of a parabola. The parabola is attatcehd to a H section bent in form of a circle such that the center of circle and focus of parabola lie at the same point. I want to know how to calculate the moment of inertia for the whole assembly
  48. R

    Impose Uniqueness on Diagonalization of Inertia Tensor?

    Given an inertia tensor of a rigid body I, one can always find a rotation that diagonalizes I as I = RT I0 R (let's say none of the value of the inertia in I0 equal each other, though). R is not unique, however, as one can always rotate 180 degrees about a principal axis, or rearrange the...
  49. 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...
  50. 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
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