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
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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 ...
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...
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...
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...
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...
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?)...
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...
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...
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?
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
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...
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...
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...
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...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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)...
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...
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...
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...
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...
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...
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...
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]
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...
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...
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...
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...