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.
Homework Statement
find the moment of inertia about the origin for the lamina which the surface of sphere (x^2) + (y^2) +(z^2) = 9 . z>2 . Given that density is a constant . Here's my wroking
The ans is 16pi (k) , but my ans is different , is my ans wrong ?
If so , which part is wrong ?
I...
Homework Statement
Show that a hollow cylinder of radius R_1, outer radius R_2, and mass M, is I=1/2M(R_1^2+R_2^2) if the rotation axis is through the center along the axis of symmetry.
Homework Equations
$$dm = \rho dV$$
$$dV = (2 \pi R)(dR)(h)$$
The Attempt at a Solution
I was mainly...
If an object is heavier.. it has more resistance to inertia..
during seismic movement.. when the ground shakes or accelerates.. does it mean bigger foundation would be more resistant and move less.. and smaller foundation can move more?
Hi,
I understand the mechanics of jumping straight up and landing on the same spot when inside of a moving bus traveling at a constant velocity but what happens when I jump straight up when skateboarding downhill? Do I land on the same spot on the skateboard, do I land further back relative to...
Homework Statement
I'm in need of a more conceptual answer, rather than numerical.
Say you have a block on a horizontal frictionless table (block 1). Then you have a string tied to block one and strung over a pulley that is at the right end of the table (the pulley has mass). On the other...
When calculating the moment of inertia for a rotating object, why is "dr" not incorporated into the integral? However, dm is part of the integral, isn't the distance from the axis of rotation changing as well? Hence shouldn't the integral involve both dm and dr?
Homework Statement
Hello,
I am looking to determine the moment of inertia for the cantilever beam pictured below. I want I to be a function of L1 and T1.
Known variables: L, D, P, t
Dependent variables: T2, L2
Design variables: T1, L1
Homework Equations
L2 = L - L1
T2 = T1 - t
Standard...
Homework Statement
Show that the moment of inertia of a hollow cone of mass M, radius R, and height h about its base is ##\frac{1}{4}M(R^2+2h^2)##
Homework Equations
##I=\int r^2dm##
where r is the perpendicular distance from the axis
Surface Area of a cone ##= \pi R (R^2+h^2)^{1/2}##
The...
is there a directly knowing the moment if the moment of inertia would be lower for an object? I am emphasizing on knowing the value of the constant value. For a sphere is 2/5 and for a cylinder 1/2, this constant values will be placed at c of cMR^2 without directly going into calculus. A...
Homework Statement
You are asked to measure the moment of inertia of a large wheel for rotation about an axis perpendicular to the wheel at its center. You measure the diameter of the wheel to be 0.600 m. Then you mount the wheel on frictionless bearings on a horizontal frictionless axle at...
1.
The mb = 25 kg block is 2 m above the ledge. The pulley is a uniform disk with a radius of 10 cm and mass m = 4 kg.
2. (a) Find the speed of the 25 kg block just before it hits the ledge.
(b) Find the angular speed of the pulley at that time.
(c) Find the tensions in the strings.
(d) Find...
Homework Statement
[/B]
Homework Equations
N/A
The Attempt at a Solution
What I am confused about is where they got the (1/4)mR^2 + (1/12)ml^2 and (1/2)mR^2 from? I am guessing that these came from the integral of y'^2 + z'^2 and x'^2 +y'^2 but I don't understand how this happened exactly...
I have a question about Special Relativity. If a person is in a rocket ship traveling at 99.999999 percent the speed of light and they are standing at the back of the ship. Will they be able to walk to the front of the ship or will inertial resistance prevent them from doing so?
I understand that some old Machian interpretations of inertia require a closed universe. Now that it has been confirmed that the universe is expanding forever and is not closed, how does Machian explanations of inertia fit in with this?
Homework Statement
In the first photo , i was told that the I represent the moment of inertia about the neutral axis ... But , in the 2nd photo , i found that the author calculate the moment of inertia about the x-axis (parallel to neutral axis ) and y -axis ( perpendicular to neutral axis) ...
Homework Statement
http://imgur.com/koz4PpI
Homework EquationsThe Attempt at a Solution
I was able to calculate the net torque on the pulley as 55.88 and the Inertia as .352. Those could be wrong, but that's as far as I could get. I really have no idea. Any kind of help/explanation would be...
I just heard something that made me realize I was taking the equivalence principle way too literally. If I were in a windowless room, and was standing on its floor, then there is, in principle, a performable experiment by which I could determine whether I was moving upward at 1 g of...
Homework Statement
A mysterious crate has shown up at your place of work, Firecracker Company, and you are told to measure its inertia. It is too heavy to lift, but it rolls smoothly on casters. Getting an inspiration, you lightly tape a 0.60-kg iron block to the side of the crate, slide a...
Homework Statement
Not sure if this is advanced, so move it wherever.
A certain rigid body may be represented by three point masses:
m_1 = 1 at (1,-1,-2)
m_2 = 2 at (-1,1,0)
m_3 = 1 at (1,1,-2)
a) find the moment of inertia tensor
b) diagonalize the matrix obtaining the eigenvalues and the...
Hello all, and forgive me if I'm making newbie mistakes as I haven't posted here much.
I realize this appears to be a homework assignment, but it is not. I am trying to develop an easy method for determining the actual moment of inertia for real wheels, for bicycles and other vehicles. I...
Homework Statement
A 1-kg standard cart collides with a cart A of unknown inertia. Both carts appear to be rolling with significant wheel friction because their velocities change with time as shown graph below:
What is the inertia of cart A?
Homework Equations
i am unsure how to even solve for...
Homework Statement
The vx(t) curves for two carts, A and B, that collide on a low-friction track are shown below:
What is the ratio of their inertias?
Homework Equations
the ratio i am looking for is mB/mA
The Attempt at a Solution
I believed that the ration was 1/2 however that is not...
Homework Statement
A thin stick of mass M = 2.8 kg and length L = 2.2 m is hinged at the top. A piece of clay, mass m = 0.8 kg and velocity V = 2.7 m/s hits the stick a distance x = 1.65 m from the hinge and sticks to it.
Q2: What is the ratio of the final mechanical energy to the initial...
I remember my teacher saying it to be the axis along the centre of mass but the centre of mass has all the mass concentrated in it and hence moment of inertia should increase as moment of inertia is proportional to mass?
Homework Statement
[/B]
There is a solar panel array of 3 panels connected to a spacecraft . The panels in the array are connected linearly (in a row: panel1 + panel2 + panel3 + spacecraft ) with hinges. They are all 0.2 meters by 0.3 meters and connected along the 0.3 meter side using 2...
So, one of my friends posed this question to me, with some background on vibrations on the Higgs Field, But, he also said that doesn't explain why matter causes inertia. As, if that accepted theory is true, it should simply create big, choppy waves. I apologize if my writing is confusing, and I...
I am not sure if this is the right place to ask it, but this is a question that I thought today, and it gave me some curiosity to understand. Imagine that a car will curve, we can say the turn is a bit tight , what are the factors that can help it to flip? I was wondering about some aspects...
Find the moment of inertia of a disc of mass m and radius r with a point mass of m on its circumference. i can't work this out can someone help me. i can work out that the moment of inertia of the disc is 1/2mr^2 but i don't know what to do with the point mass. i think it could have to do with...
I've gathered data of a skateboard going up an include and rolling back with a force plate.
- Vertical force
- Velocity
The vertical force graph looks like this:
The first bump is when the skateboard rider hits the incline.
I'm doing an investigation and I don't know how this force and...
Homework Statement
One end of a light spring with force constant k = 100 N/m is attached to a vertical wall. A light string is tied to the other end of the horizontal spring. the string changes from horizontal to vertical as it passes over a pulley of mass M in the shape of a solid disk of...
Moment of inertia is supposed to be defined with respect to a rotational axis such that for a system of point masses, I=∑miri2 where ri 's are the perpendicular distances of the particles from the axis.
However, in some derivations of the virial theorem (like the one on wiki), the so-called...
This is an experiment I have wanted to do for a few years now but don't have the necessary equipment. GR tells us if you have identical objects with the same weight exactly when they are at the same temperature, then when one object is heated, it will weigh more. This is because the...
Homework Statement
In the question , the author calculated the Ixx and Iyy , but he used the greater value (Ixx) in the calculation to calculate the shear stress , why did he do so ? why the greater value is used ?
Homework EquationsThe Attempt at a Solution
Hi everyone!
Please help, I have spent a considerable time to understand the two concepts and still this is nagging at me... I am relating to Structural Engineering, just to let you know guys. My question is ..
Moment of inertia is about distribution of mass, the further away from the axis the...
a uniform annulus consists of disc of radius 3 meters with a disc of radius 1 meters removed from its center. the mass of the annulus is m. Prove that the moment of inertia of the annulus about an axis through its center is 5m.
Hello Gurus,
What are the forces opposing rotary motion? And how to calculate them?
For eg., if we have a shaft rotating about it's own axis, are there any other forces that oppose this motion other than bearing friction, like air resistance or some other forces. And how to calculate these...
What is the moment of inertia of massless (ideal) pulley that has a string attached to its center and a mass m attached to that string?
If this pulley were hanging from a massless rope that was attached on one side to the cieling and the other side had a tension of mg, what would be the...
Homework Statement
A uniform disk of mass m and radius R lies in a vertical plane and is pivoted about a point a distance ℓcm from its center of mass in (Figure 1) . When given a small rotational displacement about the pivot, the disk undergoes simple harmonic motion.
Determine the period of...
Hello! :) ..Can you tell me why when I counting inertia the result must by in meters to the fourth power ?!
Why meters to the fourth power ?!. Is there analogical explanation?!
Homework Statement
A clock balance wheel has a period of oscillation of 0.250 s. The wheel is constructed so that its mass of 10.0 g is concentrated around a rim of radius 0.600 cm.
a) What is the wheels moment of inertia? kg m^2
b) What is the torsion constant of the attached spring? N m /...
Homework Statement
You connect a light string to a point on the edge of a uniform vertical disk with radius R and mass M. The disk is free to rotate without friction about a stationary horizontal axis through its center. Initially, the disk is at rest with the string connection at the highest...
Hi
Unit of 'moment of inertia' is kg.m^2, Which I know. But about Inertia itself, is it a quantity phenomenon or quality phenomenon? What is it's unit?
Hello i have known moment of inertia to be kg mm2 i.e. the product of mass and distance but i was looking at the euler buckling formula and it has moment of inertia in it which has units of mm4.whats the differnece between the two inertias.please help
Homework Statement
Is rotational inertia an intrinsic property of an object?[/B]Homework EquationsThe Attempt at a Solution
So I know that rotational inertia is a property of an object that deals with a resistance to a change in the state of rotational motion but is it an intrinsic property? I...
Why are some inertia units lb-in-s^2 and others lb-in^2. what the difference? The first one is from a gear box spec and the second is from a motor rotor.
Hi
Assume a Electropump which motor's moment of inertia is A and pump's moment of inertia is B.
How can calculate Electropump's moment of inertia? Is it A+B or A*B?
I am trying to determine if a function I have is working correctly. The function computes the moment of inertia for a polygon. To test the function I created a polygon that has 4 points and represents a square of 4 units by 4 units. The answer I am getting is 32. I believe the answer should be...