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.
I am stuck on what to do to calculate the inertia of a flywheel using the method described.
I am supposed to use conservation of energy equations to calculate the inertia.
I have a picture of the experiment and also the measurements I have taken.
It seems each method I try I get a different...
It's known that in inertial frame, space is isotropic. (statement of this where I have taken out of is attached as image)
When we talk about an uniform accelerated train, ground frame is considered as inertial frame(at least in newtonian mechanics). So if ground frame is considered such as...
I am at the equator with a drone capable of 1000mph speeds and the ability to hover. If the sun (or another fixed point in space) was directly overhead and I waited for the earth to rotate 1000 miles then launched the drone and flew 1000mph against the earths spin till the sun was directly...
So I have a system in which there is a disc with a moment of inertia of 1248.68. this system can rotate this disc from zero RPMs to 36 RPMs and approximately 2 seconds. How would I go about determining how much power is exerted to do said work? Many thanks
Considering a cylindrical rigid body of length 3 m and wide one. The body is rotating about an axis passing through one of its bases and perpendicular in respect to the length. At the same time, the same cylinder is orbiting about another axis parallel to the first — but distanced 10 m from the...
Hello Everybody
I'd like to set up a mechanical or electrical inertiameasurement of a Propellerarm that is in rotation, while the thrust (rpm of propeller) is rising.
Maybe with a forcespring, a pendulum, camera (timer)...
Not sure how to set it up nicely. Any suggestions?
Best
George P.
Two rotating cylinders are held in contact by a force F1. The force is applied through the center of one of the cylinders. One cylinder is the driving cylinder and the other is the driven cylinder .
Does the moment of inertia of the system depends on the force contact force F1? Why?
And...
a=2/3*g*sin(25*(pi/180))=>a=2.8507 m/s^2
vf=vi+at=>vf=0+2.8507*1.50=>vf=4.2760 m/s
So the translational motion of the cylinder is 4.2760 m/s.
4.2760=R*w
w=134.04 rad/s
PE=mgh=>PE=215*9.8*.108=>PE=227.56 J
PE = KE at the end of the roll because of energy conservation.
227.56 =...
If two plates of Aluminum (both are 2" tall, and 1/2" thick) were placed over each other (see photo 1) and then welded together all around the perimeter of the second plate (the blue one) as indicated by the yellow lines in photo 2, then would the moment of inertia be calculated as if the local...
For this problem,
How do we calculate the moment of inertia of (2) and (3)?
For (3) I have tried,
##I_z = \int r^2 \, dm ##
## ds = r ## ##d\theta ##
##\lambda = \frac {dm}{ds}##
##\lambda ## ##ds = dm ##
## \lambda r ## ##d\theta = dm ##
##I_z = \lambda \int r^3 d\theta ##
##I_z = \lambda...
How is the mass inertia product calculated? I have two examples and each one uses something different.
Example 1:
Example 2: moments and product of inertia of the cylinder
hello guys, I wanted to ask whether I can just consider/think about this as being rotation around a fixed axis in a plane representing it as if it was 'just' a rod. This is mainly so that for the kinetic energy in the second position is where if we think about it in just a plane. Is this...
Hello,
I am not sure if this is the correct forum. I was torn between Electrical Engineering and Mechanical Engineering and I thought I would start here.
I have been kicking around an idea for a DIY project and realizing I don't know enough about DC motors to find the parts I need. In this use...
Hi,
unfortunately, I am completely confused about the task
It is about the task part a
I have now defined the two rotations as follows:
The thin disc rotates around the ##z## axis, red in the picture, and then the rod to which the disc is attached rotates around the ##z_I## axis, in the...
Hi,
it's about the task e)
Since the density is homogeneous, I have assumed the following for ##\rho=\frac{M}{V}##.
I then started the proof of ##I_{23}##, the integral looks like this:
$$ I_{23}=\int_{}^{} -\frac{M}{V}r'_2r'_3 d^3r$$
Now I apply the transformation
$$ I_{23}=\int_{}^{}...
Hi,
unfortunately, I am not getting anywhere with the following task
The inertia tensor is as follows
$$\left( \begin{array}{rrr}
I_{11} & I_{12} & I_{13} \\
I_{21} & I_{22} & I_{23} \\
I_{31} & I_{32} & I_{33} \\
\end{array}\right)$$
I had now thought that I could simply rotate the...
What I did was plug in the outer radius time the force into the torque and then the mass moment of inertia is equal to m*ro^2 so then I plugged in the mass times the radius of gyration squared into I and solved for a but this is not right.
Angular Momentum and Torque are defined about a point. But Moment of Inertia of a body is defined about an axis. There are equations which connect Angular momentum and Torque with Moment of Inertia. How will this be consistent? When I say that the torque of a force acting on a body about a point...
Using the equation above I get Xcm = 0.022 m. I set the origin be at the left of the vertical rod parallel to its centre of mass as in the diagram. But I’m not sure if the equation is correct for 3d.
for the moments of inertia I am using
I = Icm + md^2
= (mr^2)/2 + md^2
where d is the...
I am reading Tensor Calculus for Physics by Dwight E. Neuenschwander and am having difficulties in following his logic regarding proceeding to derive the components of Angular Momentum and from there the components of the Inertia Tensor ...
On page 36 we read the following:
In the above text...
Hello,
I am often designing math exams for students of engineering.
What I ask is the following:
Can I choose any real 3x3 symmetric matrix with positive eigenvalues as a realistic matrix of inertia?
Possibly, there are secret connections between the off-diagonal elements (if not zero)...
I am having trouble to find the moment of inertia of the second rod!
Is it related to the first rod??
At the beginning I thought It's not!
But when took those as constant,the equation had become way much simpler and there is nothing about chaos!
My approach is given below
I placed my Oxy coordinate system at the center of the square, the ##x##-axis pointing rightwards and the ##y##-axis pointing upwards.
I divided the square into thin vertical strips, each of height ##h=2(\frac{L}{\sqrt{2}}-x)##, base ##dx## and mass ##dm=\sigma h...
Physicists say the Higgs Field is like syrup and slows particles down from the speed of light. Wouldn’t it be easier and more correct to say there are no particles, just fields, and the strength of the coupling of the electron, photon, quark etc. fields with the Higgs field determines their...
I believe I understand centripetal force, acceleration is necessary for something to spin in a circle because things normally want to continue moving in a straight line (Newton's first law), so a force is necessary to keep something rotating. If you have an object fastened to a rotating disk it...
I have come up with two different approaches, but I'm not sure which one is correct since they give different answers.
We use the following equation to get the total moment of inertia.
##I_o## = moment of inertia of disk about O axis + moment of inertia of road about O axis
Approach 1...
What kind of experiment can I design to determine the actual value of the moment of inertia. What should I instruct the sphero to do and what data should I collect?
With zero-point energy, endlessly jittering everything around randomly, nothing is ever at rest, and never moving at a constant speed (inertia).
But we've been getting along without knowledge of it for quite a while! Haha.
So, since it's random, and produces such little variations, maybe it...
We solved this problem in class as follows:
Net torque about the center of the pulley taking counterclockwise rotation to be positive = m1gR - m2gR = I_tot α, where I_tot is the moment of inertia of the full system.
My professor said that I_tot = I + m1R^2 + m2R^2, where m1R^2 is the moment...
I am completely stuck on problem 2.45 of Blennow's book Mathematical Models for Physics and Engineering. @Orodruin It says
"We just stated that the moment of inertia tensor ##I_{ij}## satisfies the relation$${\dot{I}}_{ij}\omega_j=\varepsilon_{ijk}\omega_jI_{kl}\omega_l$$Show that this relation...
$$I = \int{r^2dm}$$
$$dm = \sigma dV$$
$$dV = 4\pi r^2dr$$
$$\sigma = \frac{M}{\frac{4}{3}\pi*R^3}$$
$$I = \sigma 4 \pi \int_0^R{r^4 dr} = \frac{3*MR^2}{5},$$
which is not the correct moment of inertia of a sphere
I used the parallel axis theorem to solve the question but my answer is still wrong. Any ideas where I slipped? I can't seem to figure out the problem?
Hi everyone, I was in physics class and the professor asked if the inertia of matter changes in a black hole and I would like to know if anyone has the answer to this question.
Been 20 years since college physics. I have a problem where there are basically two inertia wheels on separate shafts coupled by a clutch. One wheel is spinning and the other is at rest. The clutch engages and connects the shafts. What's the final rpm of both wheels? I'm struggling to find a...
Initially, I calculate the moment of inertia of of a square lamina (x-z plane). Thr this square is rotated an angle $\theta$ about a vertex and I need to calculate the new moment of inertia about that vertex.
Can I split the rotated square to two squares in the x-z plane and y-z plane to find...
Hi There,
I am wanting to calculate the amount of deflection (δ) from a simply supported Beam. My Beam is an Aluminium Tube ø30mm with a 3mm Wall Thickness.
Force (F) - 500N
Length (L) - 610mm
Youngs Modulus (E) - 68 Gpa
Moment of Inertia (I) - ?
δ = F L³ ∕ 48 E I
Q1: Is this the correct...
This text refers to the photo below.
The wheel in the middle can rotate vertically without friction. The construction around it can rotate the wheel horizontally as well, also without friction.
When the blue weight is falling while the wheel is not rotating, I can calculate the kinetic energi...
This was the question
(The line below is probably some translation of upper line in different language)
For disc it was ma^2/2
For ring it was ma^2
For square lamina it was 2ma^2/3
For rods
It was different
Please explain
Thank You🙏
Hello everyone,
I'm sorry if this is not the right sub-forum to post this, but this doubt has been haunting me for a while.
I've got some rotatory machine -let's say, generic synchronous machine-. Turns out there are typical values for [kg m^2] (inertia) in the 2-10 range; the software I'm...
This is a theoretical question, not based on anything in real life, only theory. A thought experiment. Now, say that something does not have any inertia, or mass, whichever term you want to use is fine. Now, if a force were exerted on this theoretical object, how fast would it accelerate? Also...
I am stuck on problem presented about putting golf balls.
A stationary golf ball (mass=45g, dia=42mm, solid & homogeneous) is struck by a horizontal force (putter) and ignoring sliding immediately starts rolling on a level putting green. The ball eventually stops due to rolling resistance...
Help me understand a concept I came across by accident. So there is an axis (red) that is rotating with two rods attached to it (45 degrees from axis and 90 degrees with respect to one another) now if the balls at first are located closest to the red axis , as the axis begins to rotate the balls...
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.