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. R

    Rotational Inertia: Calc. & Guidance Needed

    This question is ridiculously complex for me. I know how to find the Inertia if it was a rod ##I =\frac{1}{12} ML^{2} = \frac{1}{12}(0.000104)(1.6900)^2 =0.00002475 kg * m^2## To find the Inertia for the individual disks I am having trouble. Not sure how to add them all up together. Guidance...
  2. EEristavi

    Why Do I Need to Sum All the Torques Along the Radius for Calculating Torque?

    Only problem I have is in calculating Torque I say: dT = R dF = R k g dm & dm = ##\frac m {\Pi R^2}## R dr d##\theta## However, in the solution I see that: dT = r dF = r k g dm & dm = ##\frac m {\Pi R^2}## r dr d##\theta##I don't get it: when taking the whole T (when I integrate), why do I...
  3. EEristavi

    Calculating the moment of inertia of Cone

    I'm Summing the Inertia of "donuts" with width dr and radius - r. I'm also "flattering" the cone into 2D and considering that each donut has different mass - because of the different height - h so: dm = 3 m h / (pi R2 H) dr I = ∫ dm r2 = 3 m h / (pi R2 H) r2 dr from triangle similarities H/R...
  4. R

    How is moment of inertia calculated and translated between units?

    Calculating moment of inertia and translating it between units, I've become confused. The example is a mass of 1kg at 2000mm from the pivot. The force is applied at 1000mm from the pivot. Basics as far as I'm aware: Moment of inertia = mass * Distance to center of rotation^2 Torque = Moment...
  5. S

    Are momentum and inertia definite ?

    If an object is moving it has momentum .. but if the frame of reference is altered so the speed matches, the momentum apparently vanishes (?!). Likewise with apparent inertia during acceleration of an object - similar acceleration of the frame can radically alter the perceived affect. Can...
  6. colemc20

    Hollow Sphere Inertia in Cartesian Coordinates

    Problem Statement: How do you calculate the rotational inertia of a hollow sphere in cartesian (x,y) coordinates? Relevant Equations: I=Mr^2 My physics teacher said its his goal to figure this out before he dies. He has personally solved all objects inertias in cartesian coordinates but can't...
  7. Romain Nzebele

    Is My Calculation of Moment of Inertia Using the Parallel Axis Theorem Correct?

    The picture of the problem and my attempt to solve it are below. Please let me know if my resolution is correct. Thank you in advance.
  8. badger1999

    Rotating Disk and Hanging Mass Calcululations

    I used the above equations to solve for tension, torque, inertia, and angular acceleration. Are the formulas I used correct for the given system? How can I calculate Inertia from the trendline equation, I'm drawing a blank.
  9. LeoChan

    What is the principal moment of inertia tensor for a lamina?

    The moment of inertia tensor I found out is (1/3) (-1/2) 0 (-1/2) (4/3) 0 0 0 (5/3) The principal moment of inertia tensor I found out is (1/3-I) . (-1/2) . 0 (-1/2) . (4/3-I) . 0 0 . 0 . (5/3-I) det of principal of...
  10. S

    The Effects of Incredibly Small Inertia on Acceleration: A Scientific Inquiry

    I have a question about inertia (as in mass and Newton's first law) being extremely small. Now, say the inertia of an object is, say, 0.00000000000000000000005 kilograms, or something like that. Would a light, weak force exerted on the object accelerate the object to high speeds, or would it...
  11. D

    How to calculate the moment of inertia of a bar with two masses on it?

    I first tried to calculate the moment of inertia of the bar. The problem is that I don't understand exactly how are the dimensions of the bar. The fact that it has a width ##a## means that its height is ##a##, or that it has an unknown hight and the width is ##a##, like a parallelepiped? After...
  12. K

    I What happens to the inertia of a mass falling into a black hole?

    What happens to the inertia of a mass falling into a black hole? I am not even sure if I frame the questions correctly. Will this mass reach the center or is mass distributed within the black hole? Is the singularity the whole volume of the black hole or is it a point in the center? If a large...
  13. jaewonjung

    Moment of Inertia of this combined system?

    Moment of inertia for a rod rotated around one end is 1/3ML^2 using the parallel axis theorem Moment of inertia for a sphere is 2/5 MR^2 Itotal=Isphere+Irod=2/5MR^2+1/3ML^2 However, the answer is 2/5MR^2+1/3ML^2+ML^2 Why is there an extra ML^2 added to the moment of inertia?
  14. taalf

    Formula for fictitious moments

    Hi All, Everyone knows so called "fictitious" forces, also known as "inertial" forces. They are forces felt by some mass point placed in a non-inertial frame. For example: a ball in a moving car or in a carousel. Maybe most intuitive fictitious forces are centrifugal forces, but there are also...
  15. X

    Would acceleration under water affect the person?

    I've searched online over multiple sites and can find no answer to this. I know the basics on acceleration, mass and few others. To try and paint the right picture, take a person and put him in a hollow object--a tube shape--and accelerate them. They are subject to inertia. Now take that person...
  16. S

    Combine Products of Inertia using Superposition

    I have two bodies which combine to form a system. For each body, I know its centroidal products of inertia. I wish to combine the two centroidal products of inertia to arrive at the products of inertia about the centroid of the system. Any help is greatly appreciated!
  17. Buckethead

    B Spacetime curvature due to acceleration causing gravity?

    In reviewing one of Einstein's thought experiments, the accelerating elevator in space, and the resulting bending of light passing through the elevator, Einstein's predicted that light will bend in gravity. Now Einstein's original prediction was off by a factor of 2 because he hadn't yet...
  18. D

    Moment of inertia of a branched cantilever beam

    Hey there! I am working on a project concerning the mathematical modeling of nano-swimmers in a viscous medium. Assuming the nano-swimmers to be cantilever beams, the project involves calculation of moment of inertia of the said nano-swimmers. While calculating the moment of inertia of a simple...
  19. Justin71

    Inertial force acceleration (vertical axis)

    Hi, How is the inertial force Fi (acceleration) when the system is vertical. I noted Fi_horizontal=m.a, Ff=mg.μ.cos(Θ) et Fg=mg.sin(Θ) .
  20. Justin71

    Torque Calculation for Screw Ball: TL Preload Nut

    Hi I don't understand what Fa mean ? This the weight or no ? And i don't understand too why in the torque TL, we have an additional part with the preload, the internal friction coeff of preload nut ... What is it ? Thanks.
  21. P

    Physics Experiment: Jerk & Inertia | Solving for dA/dt

    There is this experiment my high school teacher showed in physics class. You are probably aware of it (from practicalphysics.org) There is a video of a teacher actually doing the experiment here: https://sites.google.com/site/haatscience/physics/221-the-effect-of-inertia Gradually pull the...
  22. H

    Effect of time on the acceleration of an object initially at rest?

    Hello, I recently bought a Dyson vacuum and have been excitedly vacuuming my floors way more than I need to! I have been doing some thinking as well on the matter (yes, vacuuming) and have a physics problem/question. It has been a long time since I studied physics, so I am not equipped to...
  23. IanAlpace

    Moment of inertia of two rods (T shape)

    Homework Statement Hey, just wanted to ask a quick question about how to find the moment of inertia of two rods (of equal mass and length) attached together in a T shape (the axis is at the bottom of the vertical rod). My calculations got the correct result but I just wanted to check whether my...
  24. A

    Moment of inertia of a thin uniform rod

    I was thinking that if a uniform rod of mass M and length L remains static ,then it's centre of mass will be at L/2 from one end (e.g total mass assumed to be concentrated at L/2 ) But if this rod is moving with uniform angular velocity ω about an axis passing through it's one end and...
  25. K

    Problems calculating the New Moment of Inertia

    Homework Statement Posted Photo with Work done so far, but my MOI is off Homework EquationsThe Attempt at a Solution
  26. sams

    Questions Regarding the Inertia Tensor

    In Chapter 11: Dynamics of Rigid Bodies, in the Classical Dynamics of Particles and Systems book by Thornton and Marion, Fifth Edition, pages 415-418, Section 11.3 - Inertia Tensor, I have three questions regarding the Inertia Tensor: 1.The authors made the following statement: "neither V nor ω...
  27. H

    Confusion about moment of inertia

    When a question only asks for the moment of inertia (of say, a T-section), do I have to find the moment of inertia with respect to both the x and the y axis?
  28. S

    Moment of inertia of door rotation

    Homework Statement A 23 kg solid door is 220 cm tall, 95 cm wide. What is the door's moment of inertia for rotation about a vertical axis inside the door, 17 cm from one edge? Homework Equations I = I_cm + MR^2 The Attempt at a Solution I = I_cm + MR^2 I = (1/12)(23kg)(0.95m)^2 +...
  29. S

    Moment of inertia about a perpendicular axis through its center?

    Homework Statement A 15-cm-diameter CD has a mass of 21 g . What is the CD's moment of inertia for rotation about a perpendicular axis through its center?Homework Equations I = (1/2)MR^2 3. The Attempt at a Solution I = (1/2)(0.21g).((15/2)^2) = 5.9*10^-4 kg*m^2 cant see what I am...
  30. R

    Moment of Inertia of an Ammonium Molecule

    Homework Statement The ammonium ion NH4+ has the shape of a regular tetrahedron. The Nitrogen atom (blue sphere) is at the center of the tetrahedron and the 4 Hydrogen atoms are located at the vertices at equal distances L from the center (about 1 Å). Denote the mass of the hydrogen atoms by Mh...
  31. M

    I Modern Definition of Mass: Does a Photon Have It?

    If a photon does the 4 things listed below, why do we say it doesn’t have mass? I guess I’m asking if there’s a clear definition of mass. follows geodesics in spacetime (classically: accelerated in a grav field), curves spacetime (classically: creates a gravitational field), has momentum /...
  32. E

    Why does mass/energy have inertia?

    I have been googling this topic for some time, but I still don't know if this is still an unsolved mystery of physics (it's just so) or if there is a deeper underlying theory. I get the idea that mass/energy distorts spacetime, justified by thought experiments with moving objects and photons...
  33. P

    Why Can't I Get the Correct Answer Using Energy to Calculate Rotational Inertia?

    Homework Statement How come I can't get the correct answer using Energy as a way to solve this? Homework Equations 3. The Attempt at a Solution [/B] The answers use conservation of momentum which makes perfect sense and I understand that, however I used an energy approach where E(flywheel) =...
  34. DracoMalfoy

    Rotational Kinetic energy of bar, and new kinetic energy

    Homework Statement A bar of length 2.5m and mass 5kg, whose rotation point is at its center, rotates at 5 rad/s. What is the rotational kinetic energy of the bar?If a point mass of mass 1.5kg is added to each end of the bar, assuming the angluar velocity is the same, what is the new kinetic...
  35. S

    Rotational moment of inertia for 3 balls on a pipe

    Homework Statement Homework EquationsThe Attempt at a Solution i just don't know from where to take the R which is colored with brown, in the 2(MR^2), what is the R here exactly, because i took the radius of the sphere , but i get different answer althought it's near.
  36. S

    Rotational inertia hoop around a central axis

    Homework Statement Homework Equations I= mr^2 for a hoop around a central axis I= 1/12 (m)(l)^2 for thin rod about axis through center perpendicular to lenght The Attempt at a Solution I am totally confused. i said first that the three masses each will make a hoop shape so i found I=mr^2...
  37. F

    How to add area moments of inertia for varying cross sections

    Hello I am doing a shaft design layout for a spindle to minimize deflection and I have to calculate the area moment of inertia for a shaft overhang.The shaft overhang is the distance from a bearing to the end of the shaft. Here is a picture detailing the location of the overhang. The black...
  38. Swag ranger

    Acceleration in an inertial reference frame

    Homework Statement 3. (a) If an object's acceleration is zero in one inertial reference frame then is its acceleration zero in all other inertial reference frames? (b) If an object's velocity is zero in one inertial reference frame then is its velocity zero in all other inertial reference...
  39. saaaaam

    Calculate RPM given the force of a torsion spring

    Homework Statement I've got a flywheel of Inertia = 0.0019302kg/m^2 (found via solidworks), when a torsion spring is released, a force of 10N acts on the wheel via astring attached 0.065m above and 0.0325m to the right of the wheel's axis at an angle of 40 degrees. Homework Equations What is...
  40. Matthew Titus

    Calculating Motor Torque for Cricket Bat Knocking Machine

    Homework Statement Good day, i am currently working on a design project. the device is part of a cricket bat knocking machine. i need advice on how i would go about calculating the motor torque required Homework Equations Tq = Inertia x angular acceleration The Attempt at a Solution attached...
  41. N

    Inertia tensor of cone around its apex

    Im trying to calculate the principals moments of inertia (Ixx Iyy Izz) for the inertia tensor by triple integration using cylindrical coordinates in MATLAB. % Symbolic variables syms r z theta R h M; % R (Radius) h(height) M(Mass) % Ixx unox = int((z^2+(r*sin(theta))^2)*r,z,r,h); % First...
  42. P

    What is the moment of inertia for a water bottle?

    Hi, I'm setting up an equation for initial gravitational potential energy, and I'm just wondering what the moment of inertia, I, would be for a water bottle rolling down an inclined ramp? Is it mr2 or ½mr2 Or would it be something else?
  43. kasoll

    Inertia tensor v.s pincipal axes moment of inertia

    Is there a method to calculate inertia tensor form principal axes moment of inertia? Like now we have moment of inertia: (Ix,Iy,Iz)=(20,18,25), and hot to calculate the inertia tensor like (Ixx,Ixy,Ixz Iyx,Iyy,Iyz, Izx,Izy,Izz)? I have read about this page several times, but still have no idea.
  44. Exath

    Rotation of Rigid Bodies: Rotating stick with disc on top

    Homework Statement [/B] A thin cylindrical rod with the length of L = 24.0 cm and the mass m = 1.20 kg has a cylindrical disc attached to the other end as shown by the figure. The cylindrical disc has the radius R = 8.00 cm and the mass M 2.00 kg. The arrangement is originally straight up...
  45. M

    Thickness from Moment of Inertia

    Hi guys... I am creating a parametric spreadsheet to predict the behaviour of a sign post when subject to a specified wind speed for a uni assignment . Currently half way through creating the spreadsheet and one of the questions requires me to calculate a wall thickness of the pipe using the...
  46. Dante Meira

    Move a mass on frictionless surface in a vacuum chamber

    How much energy is necessary to move one kilogram of mass horizontally for one meter on a perfectly frictionless surface inside a vacuum chamber? Assuming the initial velocity of the mass is zero, the mass is at rest.
  47. D

    Experimental determination of the moment inertia of a sphere

    Hello, I was recently given the task to find experimentally the moment inertia of a sphere. I thought of rolling the sphere down an inclined plane and applying conservation of energy to the sphere. The equations i came up with are: mgh = 1/2mv2 + 1/2Iω2 solving for v^2 we come up with the...
  48. Krushnaraj Pandya

    Moment of inertia of a leftover square

    Homework Statement A square plate is of mass M and length of edge 2a. Its M.I about its centre of mass axis, perpendicular to its plane is equal to I(1). Four identical disks of diameter a are cut from the plane. The MI of leftover square about the same axis? Homework Equations 1) MI of...
  49. Math_Maniac

    Moment of Inertia of Solid Sphere - Proof

    So I have been having a bit of trouble trying to derive the moment of inertia of a solid sphere through its center of mass. Here is my working as shown in the attached file. The problem is, I end up getting a solution of I = (3/5)MR^2, whereas, in any textbook, it says that the inertia should...
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