What is Inertia: Definition and 1000 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. M

    Torque due to moment of inertia (?)

    Hi! I would like to calculate (roughly) how much torque is needed bringing the blue plateau in movement. Assume the blue plateau is loaded with 7.5 kg. The radius of the blue circle is 100 mm.
  2. K

    I How does inertia, a property of mass, arise?

    Do todays physicists have a deeper understanding on mass and inertia on how inertia arises?
  3. 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...
  4. Ang09

    Moment of Inertia with varying distance from Centre of Mass

    h = d1 + 0.08 d1 = h - 0.08 d2 = h + 0.08 I of the vertical portion = 1/12 m (l^2 + b^2) + md1^2 = 1/12 m (0.28^2 + 0.04^2) + m(h - 0.08)^2 I of the horizontal portion = 1/12 m (l^2 + b^2) + md2^2 = 1/12 m (0.28^2 + 0.04^2) + m(h + 0.08)^2 The moment of inertia for the whole T-shape about...
  5. antonov

    Moment of inertia composite body

    I have this moment of inertia problem and is a little confused on the semicircle part and if the rest is really right? I get over 10 if I calculate it in crew CAD but by hand I get 7,568032142. What is right and what am I doing wrong?
  6. Hamiltonian

    Moment of inertia of a disc using rods as differential elements

    I know there are more convenient differential elements that can be chosen to compute the moment of inertia of a disc(like rings). the mass of the differential element: $$dm = (M/\pi R^2) (dA) = (M/ \pi R^2) (2\sqrt{R^2 - y^2})(dy)$$ the moment of inertia of a rod through its COM is...
  7. R

    How Earth's rotation is changed by the change in inertia when you get out of bed

    Don't understand from where should I start?
  8. TheBigDig

    Determine the moment of inertia of a bar and disk assembly

    I have been given an answer for this but I am struggling to get to that point $$ANS = 0.430\, kg \cdot m^2$$ So I thought using the moment of inertia of a compound pendulum might work where ##I_{rod} = \frac{ml^2}{12}## and ##I_{disc} = \frac{mR^2}{2}## (##l## is the length of the rod and ##R##...
  9. P

    Moment of Inertia of a sphere about an axis

    I = 2/5M R^2 + Md^2 This is analagous to Earth's movement about the Sun. Is the moment of inertia of Earth about the centre of mass of the Earth Sun system = 2/5MR^2 + Md^2, where: M = Mass of earth, R = Radius of Earth, d = distance from Earth to centre of mass of earth-sun system.
  10. warhammer

    Question on Moment of Inertia Tensor of a Rotating Rigid Body

    Hi. So I was asked the following question whose picture is attached below along with my attempt at the solution. Now my doubt is, since the question refers to the whole system comprising of these thin rigid body 'mini systems', should the Principle moments of Inertia about the respective axes...
  11. P

    Time: Money, Stock, Moon - Inertia & Missions

    Time is money. Stocks and bonds are also money. Stocks have momentum, and thus time, which is equivalent to money, which is equivalent to stocks, has momentum, and therefore inertia. Time is also space, of course, space costs a lot of money, as does space travel. Especially space travel to...
  12. Who_w

    Moment of inertia of a regular triangle

    Please, I need help! I need to calculate the moment of inertia of a triangle relatively OY. I have an idea to split my triangle into rods and use Huygens-Steiner theorem, but after discussed this exercise with my friend, I have a question: which of these splits are right (picture 1 and 2)? Or...
  13. Leo Liu

    Computing the polar moment of inertia (calculus)

    Question: Diagram: So the common approach to this problem is using polar coordinates. The definition of infinitesimal rotational inertia at O is ##dI_O=r^2\sigma\, dA##. Therefore the r. inertia of the triangle is $$I_O=\int_{0}^{\pi/3}\int_{0}^{\sec\theta}r^2r\,drd\theta$$ whose value is...
  14. V

    Law of inertia (inertial observer and inertial frames of reference)

    I am trying to figure out what are inertial observer and inertial frames of reference. The law of inertia holds for inertial observers. Inertial observers are objects with zero net force acting on them, and move with constant velocity. Suppose we fix a set of coordinate axis in space, relative...
  15. Ranku

    Memory and Performance: The Role of Abstraction in Athletic Success

    Newton’s third law, to every action there is an equal and opposite reaction, is valid in various situations for various reasons. If an object is pushing against another object, the other object reacts with an equal and opposite force. At the same time, inertial force is also arising upon the...
  16. 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)...
  17. F

    What is the source of inertia?

    Is there a specific particle or force that gives an object inertia? Going back to the 1940's science fiction ideas of "inertialessness", is there a way to nullify or remove an objects inertia? And if so, could an inertialess object go faster than light?
  18. E

    Moment of inertia alphabet soup :)

    We start from the definition$$I_{ij} = \int_V \rho(x_k x_k \delta_{ij} - x_i x_j) dV \iff \dot{I}_{ij} = \int_V \rho (2 x_k \dot{x}_k \delta_{ij} - \dot{x}_i x_j - x_i \dot{x}_j ) dV$$Now since the rigid body rotation satisfies ##\dot{\vec{x}} = \vec{\omega} \times \vec{x} \iff \dot{x}_i =...
  19. A

    Can two coaxial motors null each other's inertia?

    Hi all! I'm new here and hoping someone who knows something about ME or Physics can help me out ... and simple terms would be nice. I am working with two servo motors and would like to minimize the "kick" they make when starting or stopping since they do it quite frequently. Please excuse my...
  20. bieon

    Pendulum, Rotational Inertia and Center of mass

    This is the figure given. My Attempt ##T=2\pi \sqrt\frac {I}{0.5gd}## ##\frac {m_r} {l} ## ##dm= \frac {m} {l}dx## ##dI = dm_r x^2## ##dI=(\frac {m_r} {l}dx)x^2## ##I= \int_l^0 (\frac {m_r} {l}dx)x^2 \, dx ## ##I_c.m=\frac {m_r l^2}{3}## ##I_,, = \frac {m_r l^2}{3}+m_p x^2## Given...
  21. S

    Tubular Column Moment of Inertia

    Can anyone explain why the moment of inertia for a tubular column in that textbook is like so? (take a look at the attachments). It should be (I = MR^2), as far as I know.
  22. C

    Moment of Inertia of a Solid Cylinder With a Wedge Removed

  23. Ugnius

    Rotating body moment of inertia

    I have done some lab work , and now i have to answer some theoretical questions , but i can not find any data about this on the web or atleast i don't know where to search , i will add some pictures of experiment for you to better understand it. I was wondering can someone share their knowledge...
  24. MattGeo

    Torque and Moment of Inertia of a Lever Arm

    I never really considered this back when I was taking physics in college but imagine for the sake of thought experiment that you have an extremely and impractically long wrench and it is fixed to the bolt you wish to tighten. Now the longer the lever arm the greater the torque so if you double...
  25. C

    Confused by Unexpected Results: Acceleration & Moment of Inertia

    Like I said, objects with the higher acceleration are giving me the lowest values. For a hoop, I got I=0.1*MR^2 For a cylinder, I got I=0.7*MR^2 this seems backwards, no?
  26. T

    Moment of Inertia with pulley and two masses on a string (iWTSE.org)

    Note: the working (taken from iWTSE website) refers to inertia as the symbol ‘J’ (in-case there was any confusion).I found equations of motion for mass m and 2m which were ‘T1 = ma + mg’ and ‘T2 = 2mg – 2ma’, respectively. I know they are connected particles with the same acceleration ‘a’.I have...
  27. wcjy

    Moment of inertia of a uniform 2D triangular plate

    Answer is 37.8 g cm^2 new to latex
  28. andyonassis

    Moment of inertia (Perpendicular axis theorem)

    So i derived the moment of inertia about the axis of symmetry (with height h) and I am confused about the perpendicular axis theorem. The problem ask to find the moment of inertia perpendicular to axis of symmetry So the axis about h, i labelled as z, the two axis that are perpendicular to z, i...
  29. S

    General Relativity and Inertia

    I haven't gone to movie theaters in 6 months. So I have to be content with online movies, and reading sci fi models, and maybe writing a short story or two. If a flying ship could travel thousands of miles per second, it can't suddenly turn 90 degrees because of inertia, the occupants would be...
  30. M

    Mass moment of inertia of a composite shape

    My thought process was to get the mass moment of inertia of the rectangle and then subtract the mass moment of inertia of the quartercircle from it. The MMoI of the rectangle is: (1/3)(0.005*7850*.6*.3)(.3^2)= 0.212 meters The MMoI of the quartercircle is: (1/4)(0.005*7850*¼π 0.3^2)(.3^2) + ? My...
  31. S

    Toy Problem to Understand Products of Inertia?

    I am a bit new to the concept of the Inertia Tensor. One question that comes to mind is, what is the physical meaning of the off-diagonals i.e. the products of inertia? I read this post : https://www.physicsforums.com/threads/physical-meaning-of-product-of-inertia.401927/post-2711721 and I find...
  32. Nexus99

    Moment of inertia of an isosceles triangle

    I did in this way: ## I = \int dm \rho^2 ## Dividing the triangle in small rectangles with ##dA = dy x(y) ## where ##x(y) = 2 ctg( \alpha ) (h - y) ## we have : ## dm = \sigma 2 ctg( \alpha ) (h - y) ## Now i have ## \rho^2 = x^2 + (h-y)^2 ## Now I don't know what I can do because it would be...
  33. 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...
  34. 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...
  35. 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...
  36. Nexus99

    Moment of inertia, center of mass and vincular reaction of a rod

    I'm struggling doing point 5, i have no idea how to solve that question. In point 1 i obtained the following result: ## I=\frac{ML^2}{2}## calculating the integral of dI, the infinitesimal moment of inertia of a small section of the rod of length dr. 2) Through the conservation of angular...
  37. Nexus99

    Moment of inertia of two coaxial disks

    The total moment of inertia is: ##I_{tot} = 2 M_1 R^2 + \frac{1}{2} M_2 R^2## We have ## M_1 = (4 \pi R^2) \sigma ## and ##M_2 = (\pi R^2) \sigma ## , where ## \sigma ## is the density of the disks. We also know that: ## \sigma = \frac{m}{ \pi 5 R^2} ## this leads us to say that: ##I_{tot} =...
  38. SchroedingersLion

    Brownian Motion - "no inertia"

    Greetings, I currently work my way through Langevin Dynamics which, in a certain limit, becomes Brownian Motion. I refer to this brief article on Wikipedia: https://en.wikipedia.org/wiki/Brownian_dynamics I understand the general LD equation given there. In order to obtain Brownian Dynamics...
  39. B

    Lead screw's moment of inertia

    In order to choose a DC motor according to the article titled: APPYING MOTORS IN LINEAR MOTION APPLICATION by PITTMAN - step 4 : "determine the total reflected inertia (Jt) back from the load to lead screw shaft " . The formula is: Jt = Jscrew + Jload. This calculation relies on the fact...
  40. G

    Does inertia have anything to do with bodies falling at the same rate?

    The equation manipulation that shows that bodies will fall at the same rate regardless of their mass is very straight forward, because mass cancels when you set F = ma of the body equal to gravitational force using Newton's gravitational equation. I have no problem understanding that in terms of...
  41. D

    Addition of moments of inertia

    Hi To calculate the moment of inertia of a large sphere , I can calculate I for a smaller sphere and then add to it , I for the spherical shell that added to the smaller sphere makes the larger sphere. Does this general process apply to all shapes ? If so , does this process have a name ie. is...
  42. Y

    Moment of inertia where mass and torque are at a different positions

    The formula for moment of inertia is: I=mr^2 A common derivation for this is: 1. F=ma 2. τ=rma 3. τ=rmrα = r^2 mα This is a rotational version of Newton’s second law, where torque replaces force, moment of inertia replaces mass, and angular acceleration replaces tangential acceleration...
  43. M

    Exploring Moment of Inertia & Angular Acceleration for Drone Propellers

    Hi, I am building a drone for a school project and I am also looking into how it flies. Recently I have been looking into angular momentum, torque, moment of inertia and angular acceleration. However I am struggling to understand moment of inertia and angular acceleration. If possible please...
  44. LCSphysicist

    How do calculate this moment of inertia?

    Inertia moment of a thin square side 2b about the center of mass... I put the coordinates in the center of the square and came to: Integral of (x²+y²)dm = Integral of (x²+y²)*(dxdy)M But, the interval of the integral is [0,b] to x and y And, since this consider just the integral of one...
  45. J

    Calculating Moment of Inertia from Ball Accelerations

    Hey guys. Im trying to figure out how to calculate the moment of inertia from a homogeneous ball based on a series of accelerations. The ball is released from the top of an incline plane (3.33 deg) and with a motion sensor, 5 values of acceleration where captured . Together with the radius and...
  46. cwill53

    How can I calculate the moment of inertia of any object?

    Apologies if I make anyone frustrated. To start, I've only had up to Calculus II so far but I was curious how to use and evaluate integrals used for moment of inertia. I know that the moment of inertia is basically an object's resistance to rotation, and is the rotational analog of mass. I know...
  47. LCSphysicist

    Moment of inertia of a cone -- Why do we divide the equation dI = dm*r^2 by two?

    Why we divide the equation dI = dm*r^2 by two when we calcule the moment of inertia of a cone relative to its symmetry axis?
  48. J

    Rotational Inertia: Hoop vs Disk

    I know that a hoop should have a higher rotational inertia than a solid disk because its mass is distributed further from the axis of rotation. What I don't understand is how a disk of the same mass and radius can have a higher rotational inertia. If the objects roll freely their axes of...
  49. Rongeet Banerjee

    Moment of Inertia for a Triangle with Masses at the Vertices

    If I take the three masses individually and try to calculate the moment of inertia of the system separately then I=(m*0²)+(m*(l/2)²)+(m*l²) =ml²/4 +ml²=(5/4)ml² But If I try to calculate Moment of Inertia of the system using its Centre of mass then As centre of mass is located at the the...
  50. Iqish

    Calculating Moment of Inertia for a Curved Rod with Respect to a Specific Axis

    Given:Thin, homogeneous, curved rod with radius of curvature 𝑅 See figure to the down. Find: The moment of inertia 𝐼𝑥′𝑥 ′ with respect to 𝑥′- the axis passing through the center of mass (point 𝐺). Can someone who can help me ?
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