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. V

    Why do the works of two objects in rotation differ when friction is present?

    Hi, I would like to compute sum of work for 2 objects in rotation, look at image please. The grey disk has a rotationnal velocity of Y rd/s. Red disks turn at X rd/s in the same direction. Red disk don't turn around itself. X > Y At time 't' friction is on. The Work for torque = Torque *...
  2. P

    Moment of inertia about a 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 = 3.3 kg and radius R = 0.26 m. The rods each have mass mr = 1.2 kg and length L = 0.72 m. What is the moment of inertia of each rod about the axis of rotation...
  3. S

    Estimate the mass of a spinning ice skater

    Homework Statement If you have data such as time of rotation when arms are extended and the lengths of their folded and extended arms measured from the centre of the skater. I know I1ω1=I2ω2 and can work out ω from the radius and time of rotation. Where can I go from here to estimate the mass...
  4. Hardik Batra

    How is the moment of inertia related to the square of the distance?

    Moment of inertia is I = MR2 object has more mass means more inertia and less mass means less inertia. That means moment of inertia is directly proportional to mass. But how the moment of inertia is directly proportional to the square of the distance.?
  5. M

    How Fast Must a Bullet Travel to Tip a Rotating Cube?

    Homework Statement A solid cube of wood with side 2a and mass M is resting on a horizontal surface. The cube is constraint to rotate about a fixed axis AB. A bullet of mass m and speed v is shot at the face opposite ABCD at a height of 4a/3. The bullet becomes embedded in the cube. Find the...
  6. J

    Two spheres mass of inertia multivariable calculus problem

    Homework Statement Let R be the solid region that is bounded by two spheres x^2 + y^2 + z^2=1 and x^2 + y^2 + z^2=2. Determine the moment of inertia of R around the x-axis if the mass density per unit volume of R is u=sqrt(x^2 + y^2 + z^2). Homework Equations Moment of Inertia around the...
  7. N

    Moment Of Inertia Of a Weld Profile

    Im needing to calculate the Zxx and Yxx for 2 shapes. The shapes are an H profile and a + profile however its not the basic profiles I am needing but the moment of inertia for the weld profile surrounding them as the theory is they are welded to a vertical metal surface then a load is applied...
  8. P

    Inertia in Space: Opening a Hatch

    Imagine that you are in a spacecraft and you then open a hatch, of a type like the door of a Gemini capsule (it hinges outward). Does the action of the hatch opening outward then hitting a stop impart force to the ship? Note that this is in deep space, that is, ignoring outside gravity fields...
  9. T

    Moments of inertia using parallel axis theorem

    Homework Statement The mass of a homogenous thin plate is 36kg. Determine it moment of inertia about the x axis Homework Equations Parallel axis theorem: Ix = Ix' + d^2*m The Attempt at a Solution p = m/a = 36/0.36 = 100 Because the density is homogenous, I found the mass of the first...
  10. Lord Crc

    Rigid body, torque and moment of inertia

    Hi, it's been quite some years since I took some entry-level mechanics at uni, and my book is no longer with me, so I'm struggling a bit here. I'm making a very simple rigid body simulator just for fun, but the angular velocity is not working out right. I suspect I've forgotten something...
  11. R

    Mass vs Inertia: Is Inertia Necessary in Physics?

    Is there any difference between mass and inertia? Is the word "inertia" necessary, or could it be eliminated from physics books?
  12. J

    Moment of inertia ice skater problem

    Problem: Consider an ice skater spinning in a circle. We will approximate the body as a cylinder with a radius of 0.25 m. The total mass of the skater is 50kg. When the skater has her arms extended we will approximate her body as a cylinder with two rods attached. Each arm is 0.75 m long and has...
  13. L

    How to Find the Components of the Inertia Tensor Matrix for Point Masses?

    Homework Statement Hi everyone, I need some help to know how to find the components of the inertia tensor matrix of a rigid body formed by a gruop of point masses attached to bars with no mass. I have 3 masses with cartesian coordenates: 1 (a,a,0), 2 (a,0,0) and 3 (-a,-a-0). The...
  14. W

    What Are Inertia Loads and How Do They Affect Aircraft Structures?

    I'm reading an old engineering book about aircraft Structures from the 1950s and I don't recognize the term inertia load. Can anyone give me a definition of it? I'm going to take a guess based on what i do know. Inertia is a body's resistance to change in speed and direction. So when some...
  15. S

    Why Is the Mass of a Wheel Concentrated on the Rim?

    A small confusion ! Why is most of the mass of the wheel concentrated on the rim ? I know that it is to increase the moment of inertia , but what is the practical use of doing so ? Thanks in advance !
  16. A

    Effects of inertia forces and friction forces on a piston in engine

    Hello, I am curious regarding the forces other than the pressure created by combustion process in IC engine.Whether inertia and friction affect worth considering or not, I want to know magnitude and nature of these forces and their effects On efficiency and performance.Thank you...
  17. P

    How to Compute the Inertia Tensor of a Cross-Hanger?

    I've done many exercises about inertia tensors of 3D bodies and sticks but now I have this exercise and I got stuck without any idea of how to do the integration to compute the inertia tensor. The statement is this: "Compute the inertia tensor of a cross-hanger consisting of 3 thin and linear...
  18. B

    Moment of Inertia of Hollow Cylinder Derivation

    For a uniform, hollow cylinder, why is this derivation wrong? M = mass of whole solid cylinder m = mass of missing cylindrical piece R = radius of whole cylinder r = radius of missing cylindrical piece moment of inertia = moment of inertia of whole cylinder - moment of inertia of...
  19. T

    Why Is Inertia Crucial in Understanding Rotational Motion?

    Why do we use inertia in rotational motion and not the whole mass of an object ?
  20. B

    Moment of inertia and torque problem

    The Question : A cylinder of mass M , and moment of inertia around its center Io, is initially rotating around its central axis with angular velocity wo. İt is gently placed on a homogeneous thin plate of mass m which rests on a smooth horizontal surface. Assume that the plate is sufficiently...
  21. deep838

    Is the Moment of Inertia strictly different

    I would like to know if there is any proof as to whether the moment of inertia for two bodies (the masses of each body are distributed on a line) about their respective center of masses, is strictly different. If not, can anyone provide me a link to where the work is computed.
  22. stateofdogma

    Moment of inertia of rectangle without dd int

    Homework Statement I found the moment of inertia of a rectangle, with the axis perpendicular and going through the center using double integration. But I also used what i thought to be an equivalent method, but it didn't work.Homework Equations dI=r^2dm \int dI The Attempt at a Solution I was...
  23. B

    Moment of Inertia for Half Disk

    1. Question: What is the moment of inertia of a thin, flat plate in the shape of a semicircle rotating about the straight side (Fig. 12.28)? The mass of the plate is M and the radius is R The diagram is attached for reference. Homework Equations Moment of Inertia: I = ∫R2dm...
  24. Greg Bernhardt

    Inertia: Definition, Equations, and Laws of Motion

    Definition/Summary Inertia is the phenomenon that a force is required to cause change of velocity. The amount of inertial mass of an object is measured by measuring how much force it takes to accelerate it. The symbol for inertial mass is m. Equations Extended explanation The...
  25. J

    Composite moment of inertia question:

    Good morning PF, I am having some difficulty finding info on calculating a composite moment of inertia. The section I am working with is 8 separate columns (WT5x15) arranged evenly spaced around the circumference of a circle. You can see what I'm taking about in the attached jpg. I found...
  26. K

    Differential moment of inertia

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  27. N

    Need help in proving this Moment of Inertia equation

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  28. G

    Inertia of door vs. braking torque?

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  29. J

    Moment of inertia of rectangular tube with welded flat bar

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  30. I

    Angular Momentum & Moment Of Inertia

    Homework Statement Two children on opposite ends of a merry-go-round of radius 1.6 m throw baseballs at the same speed of 30 m/s but in opposite directions as shown. The mass of each baseball is 0.14 kg, and the moment of inertia of the merry-go-round and children combined is 180 kg-m^2. If...
  31. J

    Gravity vs Inertia: Newton's Law of Gravitation Explained

    As it's stated in Newton's law of gravitation, every object with mass attracts all other object with a force which causes acceleration. So basically there are infinite number of forces in our universe which affect our planet as well. My question is, can an inertifal frame (which has the net...
  32. A

    The Cause of Inertia: Exploring Different Theories and Their Implications

    I am curious to know the various opinions, what ideas you favor as to the cause of inertia? What could the reference frame(s) be that induces inertial effects, and how could those effects be caused? Could the reference frame be absolute space as Newton thought, or the more relativistic idea of...
  33. H

    Moment of Inertia vs. Inertia Constant

    The following equations are found in the following reference (Page 119): http://www.eeh.ee.ethz.ch/fileadmin/user_upload/eeh/studies/courses/power_system_dynamics_and_control/Documents/DynamicsPartI_lecture_notes_2012.pdf By definition, the inertia constant for a synchronous machine is...
  34. J

    Moment of inertia of a suspended cylinder

    Homework Statement A uniform cylinder 20 cm long, suspended by a steel wire attached to its mid-point so that its long axis is horizontal, is found to oscillate with a period of 2 seconds when the wire is twisted and released. When a small disc, of mass 10 g, is attached to each end the...
  35. G

    Moment of Inertia of spherical masses

    Homework Statement Three small spherical masses are located in a plane at the positions shown below. The masses are Q=0.700 kg, R=0.400 kg, and S=0.800 kg. Calculate the moment of inertia (of the 3 masses) with respect to an axis perpendicular to the xy plane and passing through x=0 and y=-3...
  36. T

    Finding rate of change of moment of inertia tensor

    Homework Statement The Wikipedia article on spatial rigid body dynamics derives the equation of motion \boldsymbol\tau = [I]\boldsymbol\alpha + \boldsymbol\omega\times[I]\boldsymbol\omega from \sum_{i=1}^n \boldsymbol\Delta\mathbf{r}_i\times (m_i\mathbf{a}_i). But, there is another way to...
  37. J

    Finding spring constant and inertia

    Homework Statement "the question is included in the attachment" Homework Equations F=ks, E=stress/strain=(force/area)/(change in L/L) Second moment of inertia=I=(1/2)*base*height^3 The Attempt at a Solution Sice F=ks k=F/s where F=p and s= d(L) (change in L)...
  38. B

    Rotating parts of a motor have a moment of inertia

    Homework Statement The rotating parts of a motor have a moment of inertia of 15 kgm^2 and an optimum running speed of 1400 rev/min. When operating the motor is connected at optimum speed , by means of a clutch, to a shaft which has a counter rotation of 600 rev/min. The shaft has a mass of...
  39. B

    MHB Moment of Inertia: Motor, Shaft Speed & Torque Calculation

    The rotating parts of a motor have a moment of inertia of 15 kgm^2 and an optimum running speed of 1400 rev/min. When operating the motor is connected at optimum speed , by means of a clutch, to a shaft which has a counter rotation of 600 rev/min. The shaft has a mass of 80 kg and a solid...
  40. F

    Expression for the moment of inertia

    Homework Statement The thin, homogeneous bent rod has the mass m and the total length of 4b. It rotates with the angular speed of ω = ω0(24i + 12j - 6.0k) (only rotation) Determine the expression for the moment of inertia with consideration of the center of mass of the rod The figure...
  41. R

    Is the Sagnac effect a reliable measure of rotation in Kerr space-time?

    Hi, I've just started Gravitation and Inertia by Wheeler and Ciufolini. This is really a sort of trasure to me, since I was looking for something about it since when I read Einstein's relativity papers, involving Mach's principle. The main point is really simple "Inertia here arises from mass...
  42. L

    How Do You Calculate the Moment of Inertia and Stopping Time of a Yo-Yo?

    Homework Statement A yo-yo is spun from rest by pulling on the string with a constant tension of 2.0 N. The radius of the inner rod on which the string is strung round is 0.50 cm. The tension is applied for 5.0 seconds after which the yo-yo is observed to spin with an angular velocity of 15...
  43. johann1301

    Mass and inertia at high speeds

    When a particle is traveling very close to c. Will its mass actually increase and therefore its ability to resist change in its state of motion increase, OR will JUST its ability to resist change in its state of motion increase and the mass will remain the same? Will the particle just behave...
  44. K

    Calculating acceleration of gravity and inertia of irregular lamina

    Homework Statement I have a practical coming up and I have to research the method and calculations. I will be given an irregular lamina that I need to use as a compound pendulum in an experiment to determine the gravitational acceleration, g, as well as the moment of inertia (Io) of the...
  45. A

    Calculate the moment of inertia

    Homework Statement A mass m is tied with a light string,which it's another end is winded at a axle fixed at wall,in which it's radius is r. Assume there is no friction.The mass is released from rest and falls a distance S after time t. Find the moment of inertia of the axle.(represents I in...
  46. E

    Very basic statics question/moment of inertia

    Statics: If computing the moment of inertia about the y-axis of a triangular shape in the 2nd quadrant(not touching the x-axis); would i still use hb^3 /12
  47. M

    Atwood pulley and calculating inertia based on slope (m)

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  48. Z

    Relative difference between moment of inertia for the earth

    Homework Statement The Earth is slightly thicker around the equator and hence $I_{0}\neq I_{\zeta}$ I am curious in finding the angular velocity for the **precession** between using the fact that the distance between the spin axis and the precession axis is 10 meters on the surface of earth...
  49. kontejnjer

    Moment of inertia around displaced and rotated axis

    Homework Statement A homogenous disk with radius R and mass m lies in the xy plane so its center matches the origin O. Point O' is on the z axis at a distance s from point O. Axis y' passes through point O' at an angle \theta with the z axis. Find the moment of inertia around axis y'...
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