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 is a pretty hot and rarely understood topic in the automotive / racing industry.
Sure, everyone knows spinning mass on a car is worse than mass sitting in a car. its effects are greater, but by how much? Besides the benefits of the unsprung weight having less gyroscopic forces...
1. Homework Statement
A solid sphere (mass of m, radius of r and I=2/5 mr2) is rolling without slipping on
a rough surface with a speed of v. A ramp (mass of 2m and angle of θ) rests on a
smooth surface and is free to slide on the surface. As the ball rolls up the ramp, the
ramp begins to move...
Homework Statement
Find the moment of inertia of a solid cone about its longitudinal axis (z-axis)
The cone: x^2+y^2<=z^2, 0<=z<=h
I_z = \int\int\int_T(x^2+y^2)dxdydzHomework Equations
Representing the cone in cylindrical coords:
x=zcos\theta
y=zsin\theta
z=z
The Attempt at a Solution...
suppose a uniform rod of mass M and length L is at an angle B to the x axis, one end of the the rod touching the axis. wish to find moment of inertia about x axis.
let the rod touches the axis at x=0. let D=density=M/L, and I will integrate along x axis, that means that at a distance x from the...
Homework Statement
The centre of inertia (G) of a heterogeneous vehicle tyre has a distance D=0.1cm from its axis of rotation (the tyre's). The axis is referred to as Delta. The mass of the tyre is M=10kg and its radius is R=20cm. O is the center of the tyre (belongs to the axis)
Homework...
It seems to me that there are many instances of 'initial stickiness' when you move an object. Pushing a book over a table for example might be initially hard due to adhesive forces to the table which have formed over time - a plastic coating forming some kind of seal with a varnish is the...
Homework Statement
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A wheel with rotational inertia I = 1/2MR^2 about its horizontal central axle is set spinning with initial angular speed W0. It is then lowered, and at the instant its edge touches the ground the speed of the axle (and CM) is zero. Initially the wheel slips when it...
By Newton's second law of motion - inetia,we know that if we push a body in space it will keep moving forever (if nothing stops it) (am I wrong?) but when I think about conservation of energy law I am starting to have problems- let's say that I pushed a body in space,the energy converted into...
Homework Statement
For my IB higher level physics extended essay I will have to calculate the angular momentum of a cylinder rolling down a slope. The cylinder is made out of copper and will be filled with a known mass of car engine oil. I think i can obtain the angular velocity fairly easily...
Homework Statement
It has been suggested that we should use our power plants to generate energy in the off-hours (such as late at night) and store it for use during the day. One idea put forward is to store the energy in large flywheels. Suppose we want to build such a flywheel in the shape of...
Hello,
I feel very uncomfortable with some aspects of the theory of valuations, places, and valuation rings.
Here is one of my problems :
Assume that L/K is a finite Galois extension of fields, and that F is a place from K to its residual field k, whose associated valuation ring is discrete.
F...
I am having trouble with this one problem. I have tried multiple times to solve it, but come up with the same wrong answer every time. The mistake that I may be making is in finding the Inertia of the bullet entering the door: I figured that some mass at the given radius from the hinge of the...
Consider a pendulum in it's balance point hanging from ceiling. It can swing in all the directions in the space. The pendulum can only swing in a sphere(the string can't bend). Now, is it possible to release the pendulum in a particular height and with a initial condition that in the first...
Hello everyone!
New member here, as an ME major I always seem to come across very valuable information here, so I figured I would see if possibly someone here could help me.
The problem I am dealing with involves modeling a car through certain motions such as hitting a speed bump, and part...
Homework Statement
A uniform ladder having mass 14kg and length 3m is released from rest when it is in the vertical position. If it is allowed to fall freely, determine the angle Theta at which the bottom end A starts to lift off the ground. For calculation assume the ladder is a slender rod...
How do we know that moment of inertia cannot exceed MR2 for a solid body like solid cylinder, solid sphere, hollow sphere etc? R is the radius of the object in consideration.
I know it has something to do with- that for solid bodies (in some cases hollow also) there are a lot of point masses in...
What would happen if you were shot with a cannon ball in space? How badly do you reckon it would hurt, compared to if you were shot with the same cannon ball on Earth?
Hi,
I'm sorry my question is almost identical to an unanswered question here, but I was unable to reply to it (because it is old?).
I want to have the mass moment of inertia 'I'of the block C, which will be a function of theta. I am ignoring the contribution from the links.Due to the...
Homework Statement
A trapeze artist performs an aerial maneuver. While in a tucked position, as shown in Figure A, she rotates about her center of mass at a rate of 6.03 rad/s. Her moment of inertia about this axis is 16.1 kg·m2. A short time later the aerialist is in the straight position, as...
Homework Statement
A uniform, thin, solid door has height 2.2 m, width .87m and mass 23kg. Find the moment of inertia for rotation on its hinges.
2. Homework Equations
I=∫x^2dm
The Attempt at a Solution
[/B]The way I set it up was that I made into strips of length H (height) and width dr...
Homework Statement
A puck of mass 82.0g and radius 4.09cm slides along an air table at a speed of v = 1.59m/s. It makes a glancing collision with a second puck of radius 6.97cm and mass 130g (initially at rest) such that their rims just touch. The pucks stick together and spin after the...
Homework Statement
This figure shows a uniform disk, with mass M = 2.5 kg
and radius R = 20 cm, mounted on a fixed horizontal axle.
A block with mass m = 1.2 kg hangs from a massless cord
that is wrapped around the rim of the disk.
Sample problem 10-8 (has picture diagram and detailed...
Homework Statement
Half disk, radius R, mass m. I need the inertia tensor about the center of mass and then find the Principal moments of inertia about another coordinate system. Struggling with the product of inertia...
I'm working on a project involving analyzing the motion of a reciprocating saw. This saw converts rotational motion from an electric motor to linear motion by means of a slider crank mechanism. The power transmission goes from motor and attached driving gear, to crank, to connecting rod, to...
Homework Statement
You place a magnetic compass on a horizontal surface, allow the needle to settle, and then give the compass a gentle wiggle to cause the needle to oscillate about its equilibrium position. The oscillation frequency is 0.321 Hz. Earth's magnetic field at the location of the...
Homework Statement
Two particles, each of mass m, are attached one to each end of a diameter PQ of a uniform circular disk, of mass 4m, radius a with its centre at O. The system is free to rotate about a horizontal axis through A, a point on PQ such that OA = b as indicated in the diagram...
Homework Statement
A barbell that consist of a long thin rod of mass M and length L is attached to two uniform spheres on each end. Both spheres have mass M and (1/3)L. The sphere on the left is hallow (spherical shell) and the sphere on the right is solid. What is the moment of inertia for...
Homework Statement
Two particles, each of mass m, are attached one to each end of a diameter PQ of a uniform circular disk, of mass 4m, radius a with its centre at O. The system is free to rotate about a horizontal axis through A, a point on PQ such that OA = b as indicated in the diagram...
Homework Statement
The moment of inertia (I) of the bicycle wheel about the axle, can be obtained graphically using the equation:
rm(g-a) = I(a/r)+Frictional Torque. Explain how to form two variables so that, I and Frictional Torque can be obtained from a linear graph. Identify the constants...
Homework Statement
Calculate the moment of inertia for the system. The rods of length L are massless.
Image here: http://imgur.com/O639ejf
Homework Equations /answer[/B]
I know that I=ΣMR^2
The correct answer to the problem is 32ml^2
I JUST WOULD LIKE TO SEE HOW THE PROBLEM IS DONE...
Is there a formula for the moment of inertia? A thin, uniform density rod is rotating about an axis that is off the end of the rod, so it looks a bit like this:
------- |
(------- is the rod and | is the axis of rotation, so the rod is rotating out of the plane of your screen)
I just have...
Homework Statement
Disk with radius R
σ = M/A
I = ∫ mr2
Homework Equations
Today we learned how to derive various moments of inertia via density equations (M/L, M/A, M/V). I understand all of them except on how to get MR2/2 for a disk.
The Attempt at a Solution
I = ∫mr2
σ = M/A
dM =...
Homework Statement
A space station shaped like a giant wheel has a radius 95.0 m and a moment of inertia of 5.03✕ 108 kg · m2. A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1g. When 100 people move to the center of the...
Homework Statement
Taylor, Classical Mechanics Problem 10.11 **
a) Use the result of problem 10.4 (derivation of the general integral for a moment of inertia of a continuous mass distribution in spherical coordinates, using point particles) to find the moment of inertia of a uniform solid...
Hi everyone, I've been working on this problem for a while now, and I was hoping someone here could point me in the right direction. Here goes:
1. Homework Statement
A solid brass ball of mass 0.280 g will roll smoothly along a loop-the-loop track when released from rest along the straight...
Homework Statement
Homework Equations
I= ∑ miri^2 ?
The Attempt at a Solution
I'm not sure on how to start this problem. How exactly do I know which one is IA, IB, IC since it didnt specify? Can somebody please hint me in solving this problem?
Homework Statement
I'm just looking for the proper equation to use to find the moment of inertia of a complex assembly of bodies. I'm not a student and this isn't homework, but it seemed the most relevant place to pose the question.
One of my hobbies is making toys and I'm trying to calculate...
Homework Statement
For my second thread of the day I will give the weirdest problem I've encountered in physics yet.
In the mobile what is the inertia of the giraffe mgir in terms of the inertia mm of the monkey?
Homework Equations
I = md2
The Attempt at a Solution
In the picture, the giraffe...
I have a motor with rotor inertia of 140gcm2 with 71:1 gearhead.
Considering this configuration what would my inertia be at the output ?
140*(1/71)2 ??
Homework Statement
A sphere with radius R = 0.200 m has density ρ that decreases with distance r from the center of the sphere according to \rho = 3.00 \times 10^3 \frac{kg}{m^3} - (9.00 \times 10^3 \frac{kg}{m^4})r
a) Calculate the total mass of the sphere.
b) Calculate the moment of inertia...
I've to work out b & d in this equasion.
I=bd^3/12
I know that the ratio between b & d in this case is 1.166 and I am given the value of I.
It is an engineering problem as the software will only allow the use of square/rectangular or round section but we are using H section and we are allowed...
Homework Statement
I'm given the following four structures with their rotational axes marked, I have to rank them from largest to smallest rotational inertias, I have trouble with that apparently.
Homework Equations
No equations are really necessary, just my book says the more mass there is...
The force of inertia is the property common to all bodies that remain in their state, either at rest or in motion, unless some external cause is introduced to make them alter this state.Is the concept of inertia still used? When is it useful as a fictitious force?
Can you list a few situations...
Hi Folks,
Is it possible to calculate the principle moments of inertia acting along the principle axes of inertia given the moments of inertia and their directional vectors. Ie , I have the following information
Moments of inertia ##J_1, J_2,J_3=18kgm2,15kgm2,6kgm2##
and the directional...