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. G

    Understanding Newton's First Law of Motion: Exploring the Concept of Inertia

    Let's say a shovel carrying a pile of dirt is moving right and then make a sudden stop. The dirt then falls off the shovel moving in the same direction as the shovel was moving. This is an example of Newton's first law of motion. For this to happen, the net force must equal 0 on the object, so...
  2. I

    Is inertia the total gravitational forces of the Universe?

    Hi all I read a question on this subject from some time ago but was not satisfied with the clarity of the answer and in the light of recent experimental results I wish to clarify my understanding of this ancient scientific question. What is the cause of Inertia? So is inertia simply the total...
  3. M

    Problem Set Involving Inertia and Balloons

    Homework Statement 1. You are consulting for a screenwriter who is working on a science-fiction movie about the trials and tribulations of an space-faring family. She wants the script to be reasonably realistic from a scientific perspective, so she is seeking your advice on a variety of scenes...
  4. S

    Is there a named unit for inertia?

    That is, an honorific title. Eg force is cited in Newtons, charge in Coulombs, etc, as opposed to kilograms.. Generically "m" seems to be used as a symbol I guess but it overlaps with generic references to mass. eg F = ma is usually taken as referring to mass per se not inertia. But it...
  5. J

    Understanding MOI and Weight in Golf: Exploring the Optimal Balance

    At what point will weight have a diminishing effect on increasing MOI with a given size remaining the same?
  6. wolram

    B Quantised Inertia: A Solution to Dark Matter and Galaxy Rotations

    I do not know if this has been discussed before, but it is one solution to Dark Matter, Can inertia even be quatised?arXiv:1709.04918 [pdf, other] Galaxy rotations from quantised inertia and visible matter only M.E. McCulloch Comments: 9 pages, 2 figures. Published in Astrophys Space Sci...
  7. yrjosmiel

    Other symbols for rotational inertia?

    So I'm currently doing a project on motors. It just so happens that I'm dealing with both electrical current and rotational inertia. I have one small problem. The symbol for electrical current is I. But so is rotational inertia! Are there any other symbols for rotational inertia/electrical...
  8. S

    About torque and moment of inertia

    I know I just posted a topic, but I have another question. From my understanding, torque is force times the length of the lever arm, and the longer the lever arm or the more force there is, the more torque is applied. For moment of inertia, it is mass times the square of the distance from the...
  9. J

    Moment of inertia of a charged spinning top

    How can I calculate the moment of inertia of a spinning top with charge Q submerged in an electromagnetic field? I've already calculated it for the case with no charge, but I don't know how to do this.
  10. S

    Moment of Inertia of a Rotating Disk

    Homework Statement Given a non magnetic rectangular plate with dimensions: L & B. The plate is of uniform density and thickness.There are 2 points equidistant from the center of the rectangular plate along the line at B/2. Both of these pivot points have 2 disks of radius R and mass M that are...
  11. A

    Conservation of angular momentum - change of inertia

    Recently I was searching the internet and books for the connection between conservation of angular momentum and conservation of rotational energy and found nothing. Let's say an ice skater rotates and draws the arms in - the rotation speeds up. The rotational energy must increase because the...
  12. G

    Moment of inertia changes during rotation—Calculate work?

    Hi everyone, i have a question Moment of inertia changes during rotation. Calculate the work done that changes kinetic energy? Angular moment (along the axis of rotation) L = I * w A point mass M rotates along an axis attached to a mass-negligible rod, of length r. If someone moves the mass M...
  13. G

    Moment of inertia changes during rotation -- Calculate work?

    Hi everyone, i have a question Moment of inertia changes during rotation. Calculate the work that changes kinetic energy? Angular moment (along the axis of rotation) L = I * w A point mass M rotates along an axis attached to a mass-negligible rod, of length r. If someone moves the mass M at...
  14. J

    How do you calculate moment of inertia for circle?

    Hey, not sure if this is the right place to post this, but here it goes. how do you calculate the moment of inertia for a circle that is not at its center of gravity. I am trying to find the moment of inertia for a complex shape made of many circles, and this seems like a good place to start...
  15. S

    Moment of inertia of a gearbox

    I just want to check to see if I am on the right path, I have to calculate the moment of inertia of a gearbox for an application. I was thinking of breaking down the input shaft/worm into different size cylinders since the shaft has different diameters for the the input and bearings. And then...
  16. A

    Moment of inertia of a rod with balls attached

    Homework Statement Attached. Homework Equations I=mr^2, I=(1/12)m*l^2 for a rod. The Attempt at a Solution Part A I got by doing I=(1/12)3.5*(2.6)^2+2*.7*1.3^2 (I added the moment of inertia of the rod and the balls). Part B since the axis is on one of the balls, I thought we don't include...
  17. Z

    How Do I Calculate the Moment of Inertia for a Blower Shaft?

    I have a blower within a system, and I'm trying to calculate the system inertia. I'd like to get the moment of inertia for this component as would be seen by the shaft. It's shape has me a little stumped (considered perpendicular axis theorem) on what method to use for finding the inertia. Any...
  18. T

    Question about bicycles and inertia

    In a bicycle, would I be able to pedal in a gear that I can’t pedal from a stationary position in if it was already started by another power source (engine, motor or by a stronger person) whilst keeping it rotating and preventing it from stopping? So If an electric motor started moving a...
  19. M

    Determine Mass moment of inertia about any axis given Ixx...

    Hello, I am analyzing human motion. for each body segment, I have measured values for Ixx, Iyy, and Izz in local coordinate system. I want to transfer all body properties from one coordinate system to another using a transformation matrix. My question is that, is there a way to calculate mass...
  20. Spinnor

    Charged basketball, inertia ball and field

    I was wondering how much I would have to charge a basket ball of mass M, so that I would begin to feel the inertia of the electrostatic field energy. We can calculate the total electrostatic field energy surrounding the charged basket ball, call it E. Can we then equate this energy E with a mass...
  21. T

    Calculating Torque on a Rod: Net Torque, Mass & Distance

    So I've learned that the torque on an object is just: (perpendicular force)(radius) and that has worked well for things like seesaws but it doesn't take into account the torque of the object itself! In the picture the rod has a total mass of 5kg, and by definition the torque on the right is...
  22. bubsir

    Can proton mass be measured without assuming inertia?

    Direct gravitational measurements of subatomic particles seems impossible. Has it been done/tried? The mass of the proton as I know it is always "indirectly" determined by (for example) bending a beam of charged protons in a magnetic field.
  23. G

    Angular velocity tank receiving cereal

    Homework Statement The cylindrical container, when empty, has the moment of inertia of 2.0 Kgm^2 around the axis of rotation. It is rotating freely on its axis 20 revolutions per minute, when it begins to receive cereal, which falls vertically along its axis at the rate of 0.5 kg-1. The radius...
  24. G

    How to Determine Velocities for Rolling Objects on an Inclined Plane?

    Homework Statement Side by side on the top of an incline plan with height=2 meters a cylinder (Ic= MR^2/2) and a sphere (Ie=2MR^2/5) with equal radius, that come down to the base, rolling without slipping. Mass of the cylinder = 2.0 kg; Mass of a sphere=4.0 kg. Homework Equations $$K_r= 1/2...
  25. S

    Rotational Motion Question, lever arm with two masses

    Homework Statement [/B] A uniform rigid rod with mass Mr = 2.7 kg, length L = 3.1 m rotates in the vertical xy plane about a frictionless pivot through its center. Two point-like particles m1 and m2, with masses m1 = 6.7 kg and m2 = 1.6 kg, are attached at the ends of the rod. What is the...
  26. T

    Calculating the Speed of a Ball Rolling Down a Hill

    So I know that given a unchanging hill, and same mass between a sphere and cube, that the cube should slide down the hill faster (assuming negligible friction). This is observed through the energy "lost" by the sphere which instead of having all of its potential energy transferred towards...
  27. Adriano Marcato

    Output power (torque-rotation) equivalent inertia

    Homework Statement A lot of people are familiar with equivalent inertia problems, where you have a drive train and inertia on different axis and you calculate the equivalent inertia on whichever shaft you want. This time I (try to) bring something new, trying to associate the output power to...
  28. G

    Moment of Inertia: Definition & Physical Meaning

    What is the physical meaning and definition of moment of inertia?
  29. I

    Moment of inertia for a fidget spinner....

    Hi, I was just curious, how would you go about calculating the moment of inertia for a fidget spinner? I was thinking about it, and I don't know how to calculate moment of inertia for weird shapes like that. Thanks!
  30. Pbaseball

    Conservation of momentum and Moment of Inertia

    Hello everyone, I'm needing help understanding how to take the conservation of momentum equation and substitute moment of inertia inplace of mass in the equation. I understand this is a linear equation and I'm trying to incorporate angular momentum. I just want to determine the speed of the ball...
  31. T

    B Is Inertia Tied to the Stars According to Mach's Principle?

    Mach, Newton and others observed that centrifugal forces appear in a object when it rotates in relation to the stars. Einstein was convinced by this and tried, unsuccessfully as far as I understand, to incorporate what he called Mach’s Principle into General Relativity. From Wikipedia -”Mach’s...
  32. M

    Moment of inertia of a cylinder?

    Homework Statement the moment of inertia of A cylinder of height 2h radius (a) and uniform mass density ρ about a line x=y=z using multiple integration. Homework Equations I=ρ∫s^2*dV where the integral is over the volume V of cylinder and s is the perpendicular distance to the axis of...
  33. fisher garry

    A Calculate the moment of inertia of H with the probability from wavefunction

    the spin, S, for an electron is $$\frac{\hbar}{2}=5.27 \cdot 10^{-35} $$ $$\frac{2MR^2 \omega}{5}=\frac{2MRv}{5}$$ It is said that the speed of an electron is 2200 km per second and can be calculated in classical manners from electrostatic and accelerating forces on the electron from (1.11)...
  34. Megan1000

    What is the formula to find inertia with velocity and mass?

    Homework Statement v=2m/s m=10kg find the inertia At first i did 2m/s times by 10kg which is 20 but i also did 2m/s divided by 10kg =0.2 and 10kg divided by 2m/s= 5 but I'm unsure which method is correct. and momentum apparently isn't the same as inertia... Inertia is when an object carries...
  35. DevonZA

    Centre of gravity, moment of inertia and radius of gyration

    Homework Statement Homework Equations Centre of gravity: X=m1x1-m2x2/m1-m2 MOI rectangle: 1/3ml^2 MOI triangle: 1/18md^2 Radius of gyration: Ixx=mk^2 The Attempt at a Solution Mass of body 1: b*l*p = 0.8*1*10=8kg Mass of body 2: 1/2b*h*p = 1/2(0.4)*0.6*10=1.2kg1.1 X=m1x1-m2x2/m1-m2...
  36. harpazo

    MHB Moments of Inertia and More....2

    Verify the given moment(s) of inertia and find x double bar and y double bar. Assume that the lamina has a density of p = 1, where p is rho. The diagram given is a circle with radius a. The entire circle is shaded. We are also given I_o = (pi•a^4)/2, where I_o is the moment of inertia about...
  37. harpazo

    MHB Moments of Inertia and More....1

    Verify the given moment(s) of inertia and find x double bar and y double bar. Assume that the given lamina has a density of p = 1, where p is rho. I_x = (bh^3)/3 I_y = (b^3h)/3 I found the mass to be bh. x double bar = sqrt{(bh^3)/3 ÷ bh} x double bar = sqrt{b^2/3} x double bar =...
  38. harpazo

    MHB Moments of Inertia & Radius of Gyration

    Find the moments of inertia about the x-axis, y-axis and the origin. Also, find the radius of gyration about the x-axis and y-axis. y = 0, y = b, x = 0, x = a Rho = ky 1. Is ky the density function? 2. Do I integrate over dxdy or dydx? 3. Are the limits of integration y = 0, y = b, x = 0...
  39. harpazo

    MHB What is the concept of moment of inertia?

    In simple terms, what exactly is meant by moment of inertia as taught in Calculus 3?
  40. I

    Calculating the moment of inertia of a rod as a point mass

    The moment of inertia of a rod with consistent density rotating about its end is M(L^2)/3. However, if you treat the rod as a point mass and try to calculate this using mr^2, you get M(L/2)^2=M(L^2)/4. Why doesn't this work?
  41. I

    Stuck on separable equation relating to moment of inertia

    Homework Statement (a) Consider a cylindrical can of gas with radius R and height H rotating about its longitudinal axis. The rotation causes the density of the gas, η, to obey the differential equation dη(ρ)/dp = κ ω2 ρ η(ρ) where ρ is the distance from the longitudinal axis, the constant κ...
  42. B

    How to measure the moment of inertia of a motor's rotor?

    Hello, I need to measure the moment of inertia of a DC motor's rotor. Any suggestion? Thanks
  43. G

    Moments of Inertia: Hi, Need Help Understanding?

    Hi, I need some assistance understanding moments of inertia. I am doing some review for an upcoming exam, however I am slightly stumped by this question. I have already tried googling "moments of inertia" to try and understand the concept better, but I am having issues knowing when to apply...
  44. Const@ntine

    Error Transmission (Moment of Inertia)

    Homework Statement Compute the moment of intertia Io of the two cylinders, per their axis of symmetry, and then, using Steiner's formula, the moment of inertia Ib, as per the axis of rotation. Homework Equations Io = 1/2*m*R2 Ib = 2*(Io + m*x2) The Attempt at a Solution Now, this is...
  45. Arisylia

    Deriving the moment of inertia of solid sphere

    So i was going through derivations of moments of inertia of objects. For objects like the disk and rod, i was able to assume a relationship between mass and volume and integrate From there like $$ \frac{d_m}{m} = \frac{dl}{l} \\ d_m = \frac{dl*m}{l} \\ \int_{0}^{L}r^2\frac{dl*m}{l} \\...
  46. top12eaper

    Moment of inertia of cylinder with a rectangel shaped hole

    i know how to calculate the inersia for the cylinder, than i have to take away the inersia of the rectangel, but i can't find an equation for the inersia for a rectangel with the plane spinning perpendicular to the rotation axis, please help !
  47. K

    Rotational Inertia formula help

    A 24 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? I've looked at examples of how to do this problem. They connect it to center mass but I get confused when determining what the center mass...
  48. M

    I Are elementary particles subject to inertia?

    Do elementary particles have inertial mass in the same way composite objects have? If yes, does it have an impact on the motion or on the forces that act on them?
  49. R

    Calculating the moment of inertia of a solid sphere

    Homework Statement To calculate moment of inertia of a solid sphere of uniform density[/B]Homework Equations $$ I = \int r^2 dm$$ The attempt at a solution I consider an elemental disk of small thickness ##d\theta## ##dm = \frac{M}{4/3 \pi R^3}*\pi R^2\cos^2\theta* Rd\theta##...
  50. physicsdude101

    Inertia tensor for point masses

    Homework Statement Three equal point masses, mass M, are located at (a,0,0), (0, a, 2a) and (0, 2a, a). Find the centre of mass for this system. Use symmetry to determine the principle axes of the system and hence find the inertia tensor through the centre of mass. (based on Hand and Finch...
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