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.
This question is ridiculously complex for me. I know how to find the Inertia if it was a rod
##I =\frac{1}{12} ML^{2} = \frac{1}{12}(0.000104)(1.6900)^2 =0.00002475 kg * m^2##
To find the Inertia for the individual disks I am having trouble. Not sure how to add them all up together. Guidance...
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...
I'm Summing the Inertia of "donuts" with width dr and radius - r.
I'm also "flattering" the cone into 2D and considering that each donut has different mass - because of the different height - h
so:
dm = 3 m h / (pi R2 H) dr
I = ∫ dm r2 = 3 m h / (pi R2 H) r2 dr
from triangle similarities
H/R...
Calculating moment of inertia and translating it between units, I've become confused.
The example is a mass of 1kg at 2000mm from the pivot. The force is applied at 1000mm from the pivot.
Basics as far as I'm aware:
Moment of inertia = mass * Distance to center of rotation^2
Torque = Moment...
If an object is moving it has momentum .. but if the frame of reference is altered so the speed matches, the momentum apparently vanishes (?!). Likewise with apparent inertia during acceleration of an object - similar acceleration of the frame can radically alter the perceived affect. Can...
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 can't...
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.
The moment of inertia tensor I found out is
(1/3) (-1/2) 0
(-1/2) (4/3) 0
0 0 (5/3)
The principal moment of inertia tensor I found out is
(1/3-I) . (-1/2) . 0
(-1/2) . (4/3-I) . 0
0 . 0 . (5/3-I)
det of principal of...
I have a question about inertia (as in mass and Newton's first law) being extremely small. Now, say the inertia of an object is, say, 0.00000000000000000000005 kilograms, or something like that. Would a light, weak force exerted on the object accelerate the object to high speeds, or would it...
I first tried to calculate the moment of inertia of the bar. The problem is that I don't understand exactly how are the dimensions of the bar. The fact that it has a width ##a## means that its height is ##a##, or that it has an unknown hight and the width is ##a##, like a parallelepiped? After...
What happens to the inertia of a mass falling into a black hole? I am not even sure if I frame the questions correctly. Will this mass reach the center or is mass distributed within the black hole? Is the singularity the whole volume of the black hole or is it a point in the center? If a large...
Moment of inertia for a rod rotated around one end is 1/3ML^2 using the parallel axis theorem
Moment of inertia for a sphere is 2/5 MR^2
Itotal=Isphere+Irod=2/5MR^2+1/3ML^2
However, the answer is 2/5MR^2+1/3ML^2+ML^2
Why is there an extra ML^2 added to the moment of inertia?
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...
I've searched online over multiple sites and can find no answer to this. I know the basics on acceleration, mass and few others. To try and paint the right picture, take a person and put him in a hollow object--a tube shape--and accelerate them. They are subject to inertia. Now take that person...
I have two bodies which combine to form a system. For each body, I know its centroidal products of inertia. I wish to combine the two centroidal products of inertia to arrive at the products of inertia about the centroid of the system.
Any help is greatly appreciated!
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...
Hey there!
I am working on a project concerning the mathematical modeling of nano-swimmers in a viscous medium. Assuming the nano-swimmers to be cantilever beams, the project involves calculation of moment of inertia of the said nano-swimmers. While calculating the moment of inertia of a simple...
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.
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...
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 I am not equipped to...
Homework Statement
Hey, just wanted to ask a quick question about how to find the moment of inertia of two rods (of equal mass and length) attached together in a T shape (the axis is at the bottom of the vertical rod). My calculations got the correct result but I just wanted to check whether my...
I was thinking that if a uniform rod of mass M and length L remains static ,then it's centre of mass will be at L/2 from one end (e.g total mass assumed to be concentrated at L/2 )
But if this rod is moving with uniform angular velocity ω about an axis passing through it's one end and...
In Chapter 11: Dynamics of Rigid Bodies, in the Classical Dynamics of Particles and Systems book by Thornton and Marion, Fifth Edition, pages 415-418, Section 11.3 - Inertia Tensor, I have three questions regarding the Inertia Tensor:
1.The authors made the following statement: "neither V nor ω...
When a question only asks for the moment of inertia (of say, a T-section), do I have to find the moment of inertia with respect to both the x and the y axis?
Homework Statement
A 23 kg solid door is 220 cm tall, 95 cm wide. What is the door's moment of inertia for rotation about a vertical axis inside the door, 17 cm from one edge?
Homework Equations
I = I_cm + MR^2
The Attempt at a Solution
I = I_cm + MR^2
I = (1/12)(23kg)(0.95m)^2 +...
Homework Statement
A 15-cm-diameter CD has a mass of 21 g .
What is the CD's moment of inertia for rotation about a perpendicular axis through its center?Homework Equations
I = (1/2)MR^2
3. The Attempt at a Solution
I = (1/2)(0.21g).((15/2)^2)
= 5.9*10^-4 kg*m^2
cant see what I am...
Homework Statement
The ammonium ion NH4+ has the shape of a regular tetrahedron. The Nitrogen
atom (blue sphere) is at the center of the tetrahedron and the 4 Hydrogen atoms
are located at the vertices at equal distances L from the center (about 1 Å). Denote
the mass of the hydrogen atoms by Mh...
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 /...
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...
Homework Statement
How come I can't get the correct answer using Energy as a way to solve this?
Homework Equations
3. The Attempt at a Solution [/B]
The answers use conservation of momentum which makes perfect sense and I understand that, however I used an energy approach where E(flywheel) =...
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...
Homework Statement
Homework EquationsThe Attempt at a Solution
i just don't know from where to take the R which is colored with brown, in the 2(MR^2), what is the R here exactly, because i took the radius of the sphere , but i get different answer althought it's near.
Homework Statement
Homework Equations
I= mr^2 for a hoop around a central axis
I= 1/12 (m)(l)^2 for thin rod about axis through center perpendicular to lenght
The Attempt at a Solution
I am totally confused. i said first that the three masses each will make a hoop shape so i found I=mr^2...
Hello
I am doing a shaft design layout for a spindle to minimize deflection and I have to calculate the area moment of inertia for a shaft overhang.The shaft overhang is the distance from a bearing to the end of the shaft. Here is a picture detailing the location of the overhang. The black...
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...
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...
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...
Im trying to calculate the principals moments of inertia (Ixx Iyy Izz) for the inertia tensor by triple integration using cylindrical coordinates in MATLAB.
% Symbolic variables
syms r z theta R h M; % R (Radius) h(height) M(Mass)
% Ixx
unox = int((z^2+(r*sin(theta))^2)*r,z,r,h); % First...
Hi, I'm setting up an equation for initial gravitational potential energy, and I'm just wondering what the moment of inertia, I, would be for a water bottle rolling down an inclined ramp?
Is it mr2 or ½mr2
Or would it be something else?
Is there a method to calculate inertia tensor form principal axes moment of inertia?
Like now we have moment of inertia: (Ix,Iy,Iz)=(20,18,25), and hot to calculate the inertia tensor like
(Ixx,Ixy,Ixz
Iyx,Iyy,Iyz,
Izx,Izy,Izz)?
I have read about this page several times, but still have no idea.
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...
Hi guys... I am creating a parametric spreadsheet to predict the behaviour of a sign post when subject to a specified wind speed for a uni assignment . Currently half way through creating the spreadsheet and one of the questions requires me to calculate a wall thickness of the pipe using the...
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.
Hello, I was recently given the task to find experimentally the moment inertia of a sphere. I thought of rolling the sphere down an inclined plane and applying conservation of energy to the sphere. The equations i came up with are: mgh = 1/2mv2 + 1/2Iω2 solving for v^2 we come up with the...
Homework Statement
A square plate is of mass M and length of edge 2a. Its M.I about its centre of mass axis, perpendicular to its plane is equal to I(1). Four identical disks of diameter a are cut from the plane. The MI of leftover square about the same axis?
Homework Equations
1) MI of...
So I have been having a bit of trouble trying to derive the moment of inertia of a solid sphere through its center of mass. Here is my working as shown in the attached file.
The problem is, I end up getting a solution of I = (3/5)MR^2, whereas, in any textbook, it says that the inertia should...