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.
Hello,
I was curious to know if there was some intuitive out-look on why rotational inertia depends on the distance of the mass from the axis of rotation; and why is this distance have to be squared?
Homework Statement
A sphere and a cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane and roll without sliding down the incline. Then:
A. the sphere reaches the bottom first because it has the greater inertia
B. the cylinder reaches the bottom...
What is the origin of inertia?
This is a question asked by many people. I believe even Einstein pondered on this and did put some of his thoughts in a paper, but nothing really conclusive.
In Newtonian gravity, inertia appears to be just something that is inherent to mass. However, given...
Hello again,
I am currently designing a flywheel for a 745 KW engine inertia dyno.
Basically my design requirements are so:
Max RPM: 530 RPM (=55.5 rad/s)
Flywheel Diameter: 1.7 meters
Time needed to accelerate: 60 second (to max rpm)
I need help determining the mass of the...
Homework Statement
Hi,
I have been asked to find the moment of inertia of a rolling ball. The ball can be any size and radius. I have chosen a solid ball.
The experiment says that I should roll the ball down a ramp and then measure the time it takes for the ball to roll from the end of...
I am having trouble right now with the same problem (finding Ixx and Iyy).
\begin{equation}
I_{yy} = \int(x^2 + z^2)dm
\end{equation}
where
\begin{equation}
dm = \frac{2M}{R^2 + H^2} q dq
\end{equation}
and q is my generalized coordinate that is measured from the origin down the length of the...
According to GR, the inertia of bodies is greater near masses.
- https://en.wikisource.org/wiki/Geometry_and_Experience
Has this been tested? I did not find a clear answer, the gravity tests seem to be testing other things. Can it be tested? Intuitively I think that it should be possible...
While this may seem like a silly question, I had difficulty answering it completely.
"If space is a vacuum, why aren't we somewhere else already?"
If it is truly empty, devoid of any substance or mechanism whereby it might restrain or compell the action of an entity, what keeps entities...
Homework Statement
Hey
In my assignment I am writing about beamdeflection, but there's some things i really can find out how to do.
I need to explain area moment, moment of inertia and the center of gravity, i need to explain this with the help of integration.
Under her I've inertet...
Hello everyone, (This might be a little long winded but I would very much appreciate some help on this!)
Today while in psychology class, I was thinking about a much more important subject, namely a project I want to start working on. Basically what I want to do is build a motor from the...
Homework Statement
Find the moment of inertia and center of mass of:
A uniform cone of mass M, height h, and
base radius R, spinning about its symmetry
(x) axis.
Homework Equations
I = ∫R^2dm
The Attempt at a Solution
I tried using I =∫R^2dm, solving for dm I got dm=(M/V)dV...
Homework Statement
[refer to picture, thanks]
The "L-shaped" figure rotates on the axis which which intercepts through 9 kilogram and 2.5 kilogram masses. Find the moment of inertia of the object for this type of rotation. Disregard the masses of connecting bars.
Homework Equations
MR^2...
Homework Statement
I was wanting to see if someone could check my calculations. I've checked out the Iy and Ix in Autodesk Inventor and what I got is wrong.
Here are the links to my images. I apologize, the uploading option is not allowing me to upload the pictures...
Homework Statement
An object with a mass of m = 5.10 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.250 m and mass M = 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center. The...
Homework Statement
I was given a formula sheet that shows the moment of inertia equations for three shapes: rectangle, circle, and triangle. Homework Equations
There seems to be two sets of MOI equations.
Here are the rectangular equations:
Rectanglular:
Ix=\frac{bh^3}{3}...
hi everyone! I'm very confused about inertia matrix... i searched all over the web but didn't find a concise explanation of why it is useful to use it.
What's used for ? When should i use it ? the wikipedia explanation is too formal and it's difficult for me to understand... so can somebody...
Homework Statement
Consider a solid homogeneous object taller than its wide, with the top and bottom parallel. Prove that the shape with the lowest moment of inertia about an axis through the object is a cylinder with the axis through its axis of symmetry.
density, mass, and height are...
Here's a derviation from HyperPhysics:
He says:
dV=πy^{2}dz
However, if we're finding the surface area of the sphere:
dA=2πRdz≠2πydz
If we cannot use dA=2πydz, how come dV=πy^{2}dz is still applicable?
Hello guys,
I am calculating Bending and Shear stresses in hollow beams. We have a particular kind of shell that we use for impact loading, so we put rubber discs around the steel shell.
So my question is, how will it affect the moment of inertia ? Since I know that the rubber discs will...
Homework Statement
A 1.3 kg block is tied to a string that is wrapped around the rim of a pulley of radius 7.2cm. The mass of the pulley is 0.31kg. The block is released from rest. If the velocity of the block is 3.0m/s after it falls 0.5m, what is the moment of inertia for the pulley?[/b]...
Homework Statement
Question is about buckling, so i know i need to work out I (moment of Inertia), which is for a hollow tube.
Homework Equations
So the paper states..I = (0.08^4 - 0.06^4)∏/64 = 1.37 x 10^-6 m4
When i do that on my calculator, i don't get this answer. Puzzled...
Homework Statement
Find the moment of inertia, Iy, about the y-axis using a vertical strip, width dx.
Use the given equation and eliminate constants k and c, express answer in terms of number and powers of a and b.
Homework Equations
I can't figure out how to eliminate the constants...
I took a picture of the question to help.
I know that the moment of inertia for a rod (at one end, not the center) is:
1/3ML^2
And I know that the period of oscillation is:
T=2∏√(L/g)
But I don't know how to relate them... I tried doing Torque=Iα=Fdcosθ and solve in terms of...
Basically, for a standard flywheel (heavy Metal disc), Is its moment of inertia a fixed internal quantity for that flywheel which doesn't change dependent on angular velocity etc?
Hello everyone! Here is the link to the problem:
http://i.imgur.com/2HNrQ.jpg
I don't even know where to start. Any help to get started would be greatly appreciated. Thank you so much.
Cheers
Can someone please explain to me what moment of inertia means??
I googled it and I found that moment of inertia is an objects resistance to angular momentum? What does that mean exactly? Can someone please briefly explain to me (in English) what it means or give me an example? Because I really...
Homework Statement
This isn't homework but its part of my assignment. I am creating a center of gravity calculator for a car using excel which I can enter the locations of different components and their masses, and it will give me the center of gravity for the car. I am then using this to...
Hello everyone, I have been working on a problem and I am having a hard time figuring out if this is the right answer.
Homework Statement
A solid sphere of mass 10 kg and radius 10 cm is rotating about its axis.
A. Find its moment of inertia
B. What is the kinetic energy of the sphere if it...
Homework Statement I'm trying to settle an argument about front wheel drive vehicles and acceleration vs inertia and traction. Homework Equations
My position is that the faster a FWD car accelerates, the more inertia causes weight transfer off of the front wheels, and onto the rear wheels...
A) A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the side with length b.
Express your answer in terms of given...
Homework Statement
So the problem starts out like this
Stick of the Gods! You hold one end of a stick, but it has no other end. It simply extends into infinity. Its one-dimensional density distribution is given by:
λ=(λinitial)times(e^(-x/L))
λ is the density
The problem doesn't state what...
I was working out a conceptual question that asks: if a disk and a hoop of equal mass and radius start from the top of a ramp, are realeased at the same time, and roll without slipping, which one reaches the bottom of the ramp first?
Disk: I = 1/2(m)(r^2)
Hoop: I = mr^2
So the inertia...
A wheel of radius 0.20 m is mounted on a frictionless horizontal axis. A massless cord wrapped around the wheel is attaches to a 2.0 kg block that slides on a horizontal frictionless surface inclined at angle θ = 20 degrees with the horizontal. The box accelerates down the surface at 2.0...
Homework Statement
I am trying to find the moment of inertia of a disc (let the mass be m and radius R) inclined at an angle θ to the vertical axis.
(See attachment 1)
Homework Equations
The Attempt at a Solution
I started by taking a small element of area dA. (see attachment 2)
The mass of...
Homework Statement
A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. (Consider up and to the right to be the positive...
Homework Statement
In a particular coordinate frame, the moment of inertia tensor of a rigid body is given by
I = {{3,40},{4,9,0},{0,0,12}}
in some units. The instantaneous angular velocity is given by ω = (2,3,4) in some units. Find a rotation matrix a that transforms to a new coordinate...
A uniform disk(I=.5mr^2), hoop(I=mr^2), and sphere(I=.4mr^2), all with the same mass and radius, can freely rotate about an axis through the center of mass (CM) of each. A massless string sis wrapped around each item. The string is used to apply a constant and equal tangential force to each...
What is "moment of inertia?"
Just curious and I use it a lot but I am not entirely sure what it is. Call me an idiot but I need to know before my physics endeavors proceed.
Homework Statement
Four point masses form a rigid body (they are connected by massless rigid rods) given the positions M1= 3kg (2m, 4m, 0m) M2= 2kg (1m, -4m, 0m) M3= 1kg (10m, 2m, 0m) M4= 5kg (-5m, 2m, 0m)
Find:
A) Moment of inertia of this system when it rotates about x axis
B) Moment of...
Homework Statement
The total length of the composite body is 4.5 feet. Before the propellant is burned, the projectile weighs 23 lbf. After the propellant burns, the remaining projectile weighs 16 lbf. Before the propellant is burned, the mass center is located 2.6 feet from the projectile...
Hello
how can I find the moment of inertia of a circular sector about the X axis , which the sector is symmetrical about , with -θ down and θ above ?!
I_{x} = ∫y^{2} dA = ∫y^{2} *y *dx
Or =∫∫ y^{2} dy dx
I don't know how to put the limits of integration , I turned it to polar...
I'm getting desperate. The professor has assigned a project and has not clearly explained how to derive the answers. I'm doing the best I can but his TA's and recommended tutors for the class are always incapable of reproducing the answers either. It's a junior level dynamics class, but he's...
What are they? I have some poeple telling me that for a cylinder it's I = (1/4)MR2 + (1/12)ML2 and that for a disk it's the same. Other people have told me that it's I = (1/2)MR2 for a disk and that it's the same for a cylinder. In the past I've used the former and have gotten the right answers...
Homework Statement
A uniform beam of mass m = 0.6 kg and length L = 0.3 m can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F1 = 1.5 N, F2 = 1.5 N, F3 = 1.5 N and F4 = 1.5 N. F2 acts a distance d = 0.12 m from the center of...
Homework Statement
When calculating moment of inertia of a disk there is something that really bothers me. I've googled this a lot and everywhere i look they 'assume' that the Δa = Δr*2∏r, formula for rectangle, not circle: (area of circle r+Δr - area of circle r) Δa = ∏(r+Δr)^2 - ∏r^2 = ∏r^2 +...
Homework Statement
A closed cylindrical tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tube is rotated about a perpendicular bisector, the moment of inertia of water about the axis
a)increases
b)decreases
c)remains constant
d)increases if the...