Inertia Definition and 122 Discussions

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. S

    I Explaining how the Higgs fields gives particles mass

    Physicists say the Higgs Field is like syrup and slows particles down from the speed of light. Wouldn’t it be easier and more correct to say there are no particles, just fields, and the strength of the coupling of the electron, photon, quark etc. fields with the Higgs field determines their...
  2. G

    Movement of a Ball Bearing within a cavity inside a Projectile

    Summary:: Question concerning the behavior of a ball bearing inside a projectile fired straight up or at an arc. Within a projectile is a 1-inch cylindrical cavity, inside of which is a steel ball bearing that can freely roll along the length of the cavity. When the projectile is fired...
  3. J

    Electromagnetic inertial reaction force?

    I accelerate charged particle ##A## causing virtual photons to travel to distant charged particle ##B## which feels an electromagnetic force proportional to ##A##'s acceleration (for a classical field description of this effect see https://www.feynmanlectures.caltech.edu/I_28.html Eqn 28.6)...
  4. Stephen Bulking

    What happens when a car turns?

    A car moving at constant speed is in uniform circular motion, thus having centripetal acceleration of ##a=\frac{v^2}{R}##. The force associated with this acceleration is known to be friction. But friction, in nature, appears as an opposition to the relative motion between two surfaces whether it...
  5. J

    I Changing the effective mass of an electron using electric potentials?

    The Dirac equation for an electron in the presence of an electromagnetic 4-potential ##A_\mu##, where ##\hbar=c=1##, is given by $$\gamma^\mu\big(i\partial_\mu-eA_\mu\big)\psi-m_e\psi=0.\tag{1}$$ I assume the Weyl basis so that $$\psi=\begin{pmatrix}\psi_L\\\psi_R\end{pmatrix}\hbox{ and...
  6. J

    I Does General Relativity explain inertia?

    As far as I understand it general relativity does not explain the origin of the inertial mass ##m_i## in Newton's law of motion ##\vec{F}=m_i\ d\vec{v}/dt## but rather it simply applies the concept to curved spacetime. For example if we have a particle with inertial mass ##m_i## and charge...
  7. xWaldorf

    Mass and gravity -- Why do different masses accelerate the same in a gravitational field?

    So, this may be a really stupid question, and I strongly feel as though I'm missing something here. How can it be that objects of different masses have the exact same acceleration when mass is in fact resistance to acceleration? And then, if in (a vaccum) I throw upwards M and m ( a bigger and a...
  8. A

    Harmonic motion of four meter sticks

    inertia of center = [(1/12) m*L^2 + m(L/2)^2]*4 inertia of center = (4m*L^2)/ 3 inertia around pin = (4m*L^2)/ 3 + 4m(L/ 2^(1/2) )^2 inertia around pin = (10m*L^2)/ 3 inertia around pin = (10*0.1*1^2)/ 3 = 0.33 kg*m^2 d= 1/2^(1/2) = 0.707m (m*g*d/inertia)^1/2 = 2pi/period...
  9. A

    Torque and inertia of a wooden rod

    ∫ λ(x)=0.2 kg/m + 0.061(x/L)^2 kg/m = 0.2(x) + (0.061/3) (x^3) /(1/L^2) mass of rod = 0.2+ (0.061/3) =0.22 kg inertia of rod through nail = (1/3) (mass) (L)^2 inertia of rod through nail = (1/3) (0.22kg) (1m)^2 = 0.073 kg*m^2 torque magnitude = (53N) (0.5m) = 26.5N*m angular...
  10. F

    Momentum of intertia for a dihydrogen molecule

    I don't know if the value for distance between protons given in the homework is right (##d = 74.14 pm##). Indeed, on the following link : https://brainly.in/question/7147660 , they take a distance equal to ##d = 4\times10^{-10} m##. In all cases, the same formula is applied ...
  11. EEristavi

    Inertia & 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...
  12. 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 cant...
  13. 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.
  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. 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...
  16. 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) .
  17. Justin71

    Screw ball torque

    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.
  18. P

    Jerk and Inertia

    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...
  19. 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 im not equipped to answer...
  20. M

    I Modern definition of mass

    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 /...
  21. 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...
  22. 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...
  23. 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...
  24. 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...
  25. Matthew Titus

    Inertia Torque

    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...
  26. 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...
  27. 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.
  28. Metahedron

    What torque do I need?

    Good day! How do I calculate how much torque I need in a motor for my project? I must rotate a 100lb propellor, which is 11 ft in diameter, at 1 rpm .
  29. C

    Body force vs Inertial force

    Hello everyone. This is my first time on the physics forum, but I think I'm going to be a regular here. I was reading a paper that outlined various ways to approach solving dynamic problems. The first approach outlined by the author is D'Alembert's principle of virtual work. In describing...
  30. P

    Period of a physical pendulum with a pivot at its center

    Homework Statement The picture illustrates a simple pendulum and and two physical pendulums ,all having the same length ,L. Class their period in ascending order. Homework Equations T = 2π / ( I/mgh) I = Icm + mh2 Icm=(ML2/12) The Attempt at a Solution I have found the period for first...
  31. Jan Nebec

    B Does gravitational mass also change with velocity?

    Hello! The equation for relativistic mass by special relativity tells us the relativistic mass for object in motion...but since inertia mass has same value as gravitational, does this formula also apply for gravitational mass? Thank you!
  32. phantom lancer

    Physics Word Problem: Arrow and moving target collision

    Homework Statement Find the 2 unknown variables.[/B] Homework Equations Am I doing this right? Can someone help me find the solution?[/B] The Attempt at a Solution To compute for the velocity of the target/arrow combination immediately after the collision...
  33. Skrphys

    B Table cloth trick

    I have my students doing a lab where they have to do and explain the tablecloth trick using Newton’s Laws. The problem I am having is that the one question asks why the quick removal of the tablecloth matters. I know friction is not affected by speed and yet this is the only force acting on the...
  34. Cruzo

    PID tuning of hydraulic drives with high inertia

    Hi there. I have a question about the tuning of a PID (PI) controller in hydraulic drive trains with high inertia. I have a system with a 100kW hydraulic motor with an installed on its shaft encoder. That is how I am getting feedback from it. Not surprisingly I have a controller for acquisition...
  35. Andres Padilla

    Find the force P such that the disk rolls without slip

    Homework Statement When a disk rolls in a surface whitout slip, the velocity of the disk's edge (where it contacts the surface) is zero with respect the surface and the friction force is less than the maximum allowable of Us.N, where Us is the coefficient of static friction and N is the normal...
  36. H

    Inertia of a system

    Hi, in the following problem, I need to find the inertia of the system. The axis of rotation passes through the center of mass ( the pink dot). I understand that I will be equal to 4(mr^2). However, I do not understand why r= 3 (6 divided by 2) and not sqrt13 ( half of the diagonal of the...
  37. ang__

    Multiple inertia matrices

    Homework Statement The object is made out of multiple parts. The inertia matrices of every part are given. Only one part is rotating. How do I find the total inertia matrix. Homework Equations The Attempt at a Solution I thought that I could sum the inertia matrices, after tranforming them...
  38. yavorh

    Mass moment of inertia of an airplane about its main gear

    Homework Statement Okay, so this isn't so much a problem as a design issue while following an example given in a book. (Relevant material is here: http://www.aero.us.es/adesign/Slides/Extra/Stability/Design_Control_Surface/Chapter%2012.%20Desig%20of%20Control%20Surfaces%20(Elevator).pdf ) Now...
  39. 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...
  40. 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...
  41. Z

    Moment of Inertia for a blower

    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...
  42. T

    Torque on a rod?

    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...
  43. 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...
  44. 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...
  45. T

    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...
  46. G

    Moments of inertia

    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...
  47. F

    Inertia and Rotation

    Homework Statement The question is uploaded. Value of g = ## \small \rm 10~ms^{-2}## Inertia of the individual square lamina = ## \rm \small \frac{1}{12}mr^2 ~kgm^{2}## The Attempt at a Solution $$\ C=Ia$$ $$\ Moment~of~Weight~of~Particle=1.594a$$ $$\ 0.3*2g=1.594a$$ $$\ 6=1.594a$$ $$\...
  48. S

    Inertia matrix of my robot is non invertible under some conditions...

    Hello, What could be wrong when the total inertia matrix of a robotic manipulator is non invertible when under certain values of the joint angles? Thank you
  49. John Morrell

    I If Mass is relative, is "gravitational" mass relative?

    I was thinking through a thought experiment which led me to conclude that mass is relative. My thought process was basically this; there are two objects moving past each other. In the reference frame of either object, they are at rest and the other object is moving. Since the other object is...
  50. F

    SHM question

    Homework Statement Question is provided The Attempt at a Solution The required solution is provided My question is, the examiner have used sine theta in their expression for change in potential. I keep ending up with 1 - cosine theta Second question is how did they get rid of theta in the...
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