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. B

    Rotational kinetic energy / moment of inertia

    Homework Statement A thin, cylindrical rod = 27.0 cm long with a mass m = 1.20 kg has a ball of diameter d = 10.00 cm and mass M = 2.00 kg attached to one end. The arrangement is originally vertical and stationary, with the ball at the top as shown in the figure below. The combination is...
  2. L

    Moment of inertia rolling down a hill

    Homework Statement Two solid spheres -- a large, massive sphere and a small sphere with low mass -- are rolled down a hill. Which one reaches the bottom of the hill first? Homework Equations ICM= (2/5)MR2 The Attempt at a Solution I thought that this would be the smaller sphere...
  3. L

    Designing a Car for Coasting Race: Wheels

    Homework Statement Suppose you are designing a car for a coasting race -- the cars in this race have no engines, they simply coast down a hill. Do you want large wheels or small wheels? Do you want solid, disk-like wheels, or hoop-like wheels? Should be wheels be heavy or light? (Select all...
  4. T

    Moment of Inertia of Half a Sphere

    Homework Statement Homework Equations I_a = I_G + md^2The Attempt at a Solution I tried using the parallel axis theorem to find the moment of inertia about the axis. In the formula sheet they give the moment of inertia of a hemisphere: I_G = 0.259mr^2, where d, the distance from the center is...
  5. X

    Moment of inertia of a triangular plate

    Homework Statement see attachment Homework Equations integration The Attempt at a Solution answers: a. mH2/6 + mt2/12 b. mB2/2 + mt2/12 c. mH2/6 + mB2/2 d. -mBH/4 e. 0, 0 If the plate were thin t can be ignored. Ok so e is because of symmetry so I get that. a-d on the...
  6. S

    Moment of Inertia for a uniform wire

    Homework Statement A flat object shown here consists of a circle and square made of heavy, uniform wire and welded together at the corners of the square. The mass of the circle is M. The mass of the square is m and its side has a length d. To find the objects moment of inertia about Axis A...
  7. C

    Moment of inertia and rotational kinetic energy

    I can't seem to understand moment of inertia. What does it mean and how is it derived ? How does it relate to rotational kinetic energy.
  8. S

    Moment of inertia spinning disk integration

    Homework Statement I want to calculate the moment of inertia of a spinning disk via integration. I'm aware of the perpedicular axis theorem, but I want to integrate. Homework Equations I = ∫r^2dm The Attempt at a Solution if I set my coordinate axis op so that the origin of the...
  9. R

    Moment of Inertia? Potential and Kinetic Energy? Anybody awake?

    I don't know how to answer these - please please please help! Consider the following objects of mass m rolling down an incline of height h. (a) A hoop has a moment of inertia I = (1/2)mr2. What is the equation for the velocity vhoop of the hoop at the bottom of the incline? (Use the...
  10. X

    Moment of inertia (integration)

    Homework Statement See attachment Homework Equations Integrating The Attempt at a Solution The answer is 16pi slug-ft^2. Now I know your suppose to integrate it. Its in 2D, so a double integral at most, maybe a single integral? I'm not very good with integrals and their limits...
  11. M

    Calculating the Moment of Inertia of an Irregular Rod Shape

    To give you a better idea, I have it drawn out here: http://tinypic.com/r/eq6ln5/6 I am calling the thickness of a rod t and the thickness of the shaft t2. I am using the basic equation Ixx = (integrate over area)(y^2)dA on different sections and then adding them all together, following the...
  12. A

    Moment of inertia: off-central diameter

    Question for the brilliant minds around here: I'm trying to figure the amount of torque (I*a) needed to rotate a cylinder of a given mass, diameter and length around a pivot point that is off-center. Typically I'm assuming I would find it out by calculating both I for central diameter and end...
  13. B

    How to Calculate Moment of Inertia for a Solid Disk with Central Hole

    Consider a solid disk made of aluminum with a central hole as shown in the figure - can't include...don't believe it's necessary. The external and internal diameters are found to be 13 inches and 0.6 inches. The disk is 0.5 inch thick. The density of aluminum is 2.70 g/cm3. Question: Calculate...
  14. L

    Homework Help: Calculating Moment of Inertia & Radius of Gyration

    Homework Statement Homework Equations radius of gyration: r = root (I/m) I = moment of inertia m = mass parallel axis theorem given above The Attempt at a Solution Okay, so I think the moment about CM is just m*0.24^2, but after that, I'm less sure. Is the moment about the hip just...
  15. sweet springs

    Is Inertia Explained by the Higgs Mechanism?

    Hi. Mass of some particle is explained by Higgs mechanism. Is inertia also explained by Higgs mechanism? Inertia increases when a particle is in motion by relativity. Is this increase of energy is explained by Higgs mechanism? More tight binding with Higgs particle when a paricle is...
  16. H

    Mistake on wikipedia (Moment of inertia of a quadrant)

    I think i found a mistake on wikipedia about t he moment of inertia of filled circular quadrant. the link to the page http://en.wikipedia.org/wiki/List_of_area_moments_of_inertia the link to the specific object ...
  17. H

    Moment of Inertia of a uniform triangle(involves integration)

    Homework Statement The attachment shows an equilateral triangle of side length "2d" It is a uniform triangle in the 2-D space. Mass of triangle = M I have to find the moment of inertia about one of its side . I am taking the side \overline{AB} as the axis of rotation (hence i would be...
  18. N

    How Is the Moment of Inertia Calculated for a Solid Torus on the XY Plane?

    Homework Statement To calculate the moment of inertia of a solid torus through the z axis(the torus is on the xy plane), using the parallel and perpendicular axis theorem. Homework Equations The Attempt at a Solution Well, first I divided the torus into tiny little disks and...
  19. M

    Is it possible to directly compute the maximum moment of inertia for an object

    Given some arbitrary shape I can compute the moment of inertia about any axis without a problem by summing the inertia of each of the shapes making up the entire object. I also know the center of mass of the object. Is it possible to directly compute the angles of the axis for the minimum and...
  20. S

    Problem 10.30 (with Hints) - Mastering Physics - Rotational Inertia

    Homework Statement Three 2.30kg masses are located at the vertices of an equilateral triangle 55.0cm on a side, connected by rods of negligible mass. Find the rotational inertia, I_2, of this object about an axis that passes through one vertex and the midpoint of the opposite side Homework...
  21. C

    Which impractical standards we use only because of inertia?

    I'm curious which standards that are being used are only outcome of need of backward compatibility that, if we had to select once again would be selected differently. Any ideas? 1) Keyboard? Dvorak vs. Qwerty? Or is it a myth? (Or should there be a separate keyboard layout for every language?)...
  22. S

    Calculating the Inertia Tensor of a Homogeneous Sphere

    Homework Statement Calculate the moments of Inertia I_{1}, I_{2}, I_{3} for a homogenous sphere Homework Equations I_{jk}=\intx^{2}_{l}\delta_{ik}-x_{i}x_{k}dV The Attempt at a Solution For I_{x} i set up the equation using the above equation in cartesian coordinates and then i...
  23. D

    Moment of inertia of a few basic objects

    Ok i need some help with some homework that is to derive formula for moment of inertia of a few objects about the axis's that i have mentioned 1. Rectangular slab about axis through center(sides a,b) 2. Annular cylinder about central axis (radii R1 and R2) The only equation i know is...
  24. mesa

    Moment of inertia question; tube, solid cylinder on inclined plane.

    If you have a tube and a solid cylinder of the same dimensions and density and rolled them down an inclined plane the 'tube' would cover the same distance in less time?
  25. B

    How does relativity explain inertia

    Hi: Will someone please answer this question: How does relativity explain inertia. What resists accelerational force; if there were nothing resisting the motivating force, why would a force be needed at all to set it in motion. Tks
  26. E

    Moment of Inertia of a body with linearly increasing density?

    A thin wire of length L and uniformly density ρ is bent into a circular loop with center at O.The moment of inertia of it about a tangential axis lying in the plane of loop is. Ans : Mass M is not given,but ρ is given. So M=ρL3->(1) (L3 means L cube,no idea how to post it in that manner!). For...
  27. E

    Moment Of Inertia of broken disk or ring confusion

    We all know that M.I of a Uniform rigid rod about an axis perpendicular to it's length and passing through it's center is MLsquare/12.Where M is mass and L is length of the rod. If it is broken to half such that M becomes M/2 and L becomes L/2,we can't apply ML square /12 formula to it.We have...
  28. B

    Moment of inertia and force needed to tilt/change axis of rotation

    Consider a freely rotating body. Let the axis of rotation be the z-axis. For simplicity assume all the mass of the body is concentrated in the x-y-plane, i.e. the plane in which the body rotates. I have read about the moment of inertia tensor on wikipedia, but I don't see how I would combine...
  29. W

    The moment of inertia of a group of seven pennies

    Homework Statement See attached photo Homework Equations The Attempt at a Solution I figured I would use the parallel axis theorem. I'm stuck between two different methods of doing the question, both of which are choices in the answers. My gut instinct says to take the...
  30. U

    Moment of Inertia of Disc through diameter

    Homework Statement The problem is attached in the picture. The Attempt at a Solution I managed to solve it using a different method. I have no idea what the answer is talking about.. My method Found dI of a strip = (1/3)*dm*h2 then i replace h by x, then integrate from -a to...
  31. F

    Moment of Inertia of a Non-Uniform Rod?

    Homework Statement Calculate the moment of inertia of a uniform rigid rod of length L and mass M lying along the x-axis which rotates about an axis perpendicular to the rod (the y axis) and passing through it’s center of mass. The rod has a line density that is a function of location such...
  32. A

    Inertia of a pendulum with disc

    A pendulum consists of a uniform thin rod of mass 5 kg and length 2 m to which is fixed a circular disc of mass 8 kg and radius 0.4 m. There is a pivot at one end. (a) Find the CoM and Moment of Inertia when the disc is: (i) half way along the rod; (ii) at the opposite end of the rod to the...
  33. N

    Inertia with the parallel axis theorem

    Homework Statement A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center? Homework Equations Ip = Icm + Md2 Isolid sphere = 2/5MR^2 The Attempt at a Solution This is...
  34. P

    Effect of moment of inertia on rolling distance

    Hi everyone, good day. this might be a simple question, but I need someone to check my answer. A disk and a hoop, of same mass and same diameter, is first giving a torque (same amount of torque for both) then the torque is removed (the torque is acting on them for the exact same period of...
  35. D

    Gravity & Inertia: Proportional to Mass?

    If force is something that changes the state of a body and inertia is opposition to change of state how can gravitational force be proportional to mass?
  36. C

    Conservation of Angular Momentum Experiment: Moment of Inertia

    Homework Statement I did a lab where there was a rotating solid disk with mass= 0.915kg and diameter=0.253m. This was rotating horizontally with an initial angular velocity of 3 different values ω radians/second. After recording the initial angular velocity, I dropped a thin-walled hollow...
  37. R

    Moment Of Inertia (calc vs physics different answer)

    I'm trying to understand Moment Of Inertia using integration. But it seems the calculus definition of physics definition are different. (I'm trying to apply my math skill to physics) example of apparent contradiction: here:http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#mi it says the...
  38. P

    Moment of inertia of system in 3D

    Hey i am working on something and i need to know how to calculate moment of inertia of a 3D system of objects. I know these variables: Mass of whole system Center of mass of whole system Center of mass of each object Offset of each object Mass of each object Moment of Inertia of each...
  39. A

    Moment of inertia for ball rolling up a ramp.

    Homework Statement A ball with mass 1.0 kg and radius 0.20m rolls without slipping along level ground with a speed of 10 m/s. The ball then rolls up an incline reaching a maximum vertical height of 8.0 m. What is the moment of inertia of the ball? (Do not assume the ball is a uniform sphere)...
  40. C

    How Do You Calculate the Second Moment of Inertia for a Reinforced Hollow Tube?

    Hello, I am trying to calculate the second moment of inertia for a hollow tube with a reinforcement bar that goes through the tube. The cross section is basically a thin-walled circle (0.1" thickness) with a horizontal bar (about 0.1" thick for now) that spans the diameter of the circle. How...
  41. S

    Find the moment of inertia of a solid sphere.

    Homework Statement Beginning with Icm = Integral of r^2 dm from r1 to r2, find the moment of inertia of a solid sphere about any tangential axis. Homework Equations Icm = Integral of r^2 dm The Attempt at a Solution I set up the infinitesimally mass of an infinitesimally...
  42. P

    Moment of Inertia for a Square and a pipe of variable density

    Homework Statement First, there's a slender rod with length L that has a mass per unit length that varies with distance from the left end, where x=0, according to dm/dx = yx where y has units of kg/m^2. (a) Calculate the total mass of the rod in terms of y and L (Which I've already done and...
  43. johann1301

    Does Higgs-particle explain origin of inertia?

    We know that the Higgs-particle gives an explanation as to why there is mass in the universe. But mass has another property/ability. It has the ability to resist change in its state of motion. Is this ability - inertia - explained by the discovery of the Higgs-particle? Does Higgs-particle...
  44. P

    Equivalent inertia calculation problem

    Homework Statement Need to calculate equivalent mass moment of inertia of a part that moves linearly at the point where torque is applied. Please find two schematic drawings in the attachement (representing the same mechanism in a slightly different way). Basically, there is a rotating crank...
  45. H

    How can I accurately calculate the inertia of rotors with cooling fins?

    Hello Everyone, I'm new hear & am hoping that someone can help me out. I have two Rotors, one on each end of a shaft with bearings in the centre, both have air cooling fins in the centre of each rotor. I need to calculate the Inertia of these Rotors, I have looked at several formula's but...
  46. M

    Question in momentum of inertia

    http://store2.up-00.com/June12/ScF29742.jpg can please help me how I can find N1 and N2 and I don't understand what mean by Speeeeed varies from above and below ? b]
  47. A

    Find torque in the x direction given moment of inertia tensor for plate.

    This is for prelim study. Just wondering if this solution is correct. Problem A thin homogeneous plate lies in the x-y plane. Its moment of inertia tensor in the x,y,z basis is given by \textbf{I}=σl^{4}\begin{pmatrix} 2 & -2 &0 \\ -1 & 2 & 0 \\ 0 & 0 & 4\end{pmatrix} If the plate...
  48. R

    Is Momentum the Reason Behind Inertia?

    Can we say that momentum is the reason behind inertia? like momentum explains inertia. Momentum:- mass * velocity net force is the rate of change of momentum. f=mv/t and Inertia:- it is the tendency of an object to stay in the state of motion it currently is in i.e resist the...
  49. D

    Moment of inertia of a uniform solid sphere

    For calculating I of a uniform solid sphere, why can't we use thin spherical shells? When I try to use spherical shells I get (3/5)MR^2. Every single derivation uses thin cylindrical shells and end up with the correct expression((2/5)MR^2) but they never explain why it is correct to use...
  50. A

    Rotational Inertia equation help

    Homework Statement Derive the equation for the linear acceleration of a falling mass m suspended by a string from the rim of a uniform disk of mass M and radius R that is free to rotate without friction about its principal axis. Homework Equations a=rα linear acceleration = radius*angular...
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