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
This is not a specific problem, I was just wondering, what unbalanced force acts on your body when you are in a car traveling at a constant velocity and the car comes to a sudden stop? This has to do with Newton's First Law, but I'm unsure of what force applied to your body...
Homework Statement
If an astronaut was in a weighless environment, sitting down and eating a meal, what would happen to the astronaut if the spacecraft decided at that moment to turn on the space craft's main engines and
a) the astronaut was facing the engines?
b) the astronaut's back was to...
If the mass of an object is the same, does the inertia ever change. For example, is the inertia of a person different if they are on the surface of the Earth than if they are orbiting Earth or in outer space?
This isn't actually a homework problem, but I am still posting it here. I am confused by rotational inertia. How does mass distribution affect rotational inertia? Because I know it should, but I don't know how it would.
Homework Statement
I am given the equation (m1 – m2)g = (m1 + m2 + I/R2)a and the experiment is to validate this equation.
Homework Equations
The Attempt at a Solution
After following the lab guide, it tells you to plot the weight difference (m1– m2)g against acceleration and determine...
Homework Statement
hello,
i want to calculate the inertia tensor of the combination of a point mass and a sphere in the object's frame, the center of mass is at the origin. The point mass remains at the surface of the phere
The sphere is uniform, radius r and mass M, and the point mass has mass...
Would you guys agree with these websites on how orbits work?
http://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-orbit-58.htmlhttp://www.qrg.northwestern.edu/projects/vss/docs/space-environment/1-what-causes-an-orbit.html
Hi. So I know that inertia (the resistance of an object to a change in its velocity) is reliant on mass. I also know that momentum is mass times velocity. So momentum is really inertia times velocity. My question is: if that's so, is momentum then not a measure of a moving object's inertia, its...
Homework Statement
. What is the angular acceleration if a force of 3 N is applied perpendicular to the radius of a 5 kg solid sphere that has a radius of 0.6 meters?
Homework Equations
= r x F
I = mr^2
The Attempt at a Solution
I used
tried solving for angular acce.
3N/(5kg)(0.6)...
Homework Statement
I need to know why my derivation does not work. I am attempting to derive I=2/5 mR^2Homework Equations
I have seen people derive it using disks but my question is why do the shells not work? Where in my set up did I go wrong? Thanks
The Attempt at a Solution
I am attempting...
in this video
http://www.physicsgalaxy.com/lectures/1/44/234/Solved-Example-2#12(see only the question)
the method illustrated is integration but i thought of an alternate method,
moment of inertia of half disc with radius r2 is 1/2mr2^2 and that of half disc with radius r1 is 1/2mr1^2.so...
Homework Statement
I am doing the old frozen can vs liquid can experiment and one of the questions asks that if cans with different diameters were used with the same contents (so same mass relative to diameter size) how would this effect the time taken for the cans to go down a ramp (how would...
Homework Statement
Theres an object which makes a pendulum motion.Lets suppose we hang the mass to the ceiling.We released the object with inital angle 0 to the ceiling.(I mean the angle between the object and the ceiling is zero).Whats the moment of the Inertia to the point A.
A is a...
I'm having a hard time undertanding a concept of moment of inertia and Angular acceleration.
Homework Statement
We have a closed system above. M1 is a cylinder of 2 Kilograms, moment of inertia of a cylinder ( MR2 /2 ) with a string tightly rolled around it. This string connects to a free...
Homework Statement
In our physics lab we were to set up a system looking like this:
where the mass was released and the velocity/acceleration and of the ring was calculated using MotionLab software. Our goal was to find the predicted total moment of inertia by just calculating the moment of...
Homework Statement
Find the moment of inertia of these composite objects.
I've attached two different composite objects; each rod has length L and mass M.
Homework Equations
I = Icm + MD2
Long thin rod with rotation axis through centre: Icm = 1/12ML2
Long thin rod with rotation axis through...
Homework Statement
Need to find the moment of inertia of a cylinder, about its center of mass, about the three principle axes. Z axis is normal to the circular faces of the cylinder. mass = M, radius = R, height = h
Homework Equations
∑miri2
The Attempt at a Solution
The Izz for whatever...
Homework Statement
Find the moment of inertia for this composite object:
M1=5kg at (3,4) and M2=3kg at (6,8)
Homework Equations
Moment if inertia for point particle = MR2
The Attempt at a Solution
I'm not sure if moment of inertia should be componentized -- broken up into x and y...
This seems to be a crucial detail that I just glossed over, but when finding the inertia tensor of an object, is the origin always situated at the object centre of mass?
For example: In the link (http://hepweb.ucsd.edu/ph110b/110b_notes/node26.html ), is it necessary to do the integral from...
Homework Statement
The cubic is divided into 4 parts , A, B and C, D , each with thickness of 1mm , i am sked to find thesecond moment of inertia about x -axis
Homework EquationsThe Attempt at a Solution
i' m using the formula Ixx = Ix +A(d^2)[/B]
for part CD, Ixx = 50(1^3) / 12 + 50...
Homework Statement
Calculate the moment of inertia of a uniform rigid rod of length L and mass M, about an axis perpendicular to the rod through one end.
Homework Equations
Parallel axis theorem: I = Icm + MD2
Long thin rod with rotation axis through centre: Icm = 1/12 ML2
Long thin rod with...
Hi! I'm a high school student, aspiring to pursue a career in Astronautical Engineering. I always try and ponder on questions about everyday aerodynamics and physics. So, here's a question from you from an aspiring scholar.
It is known that, at high velocities, pilots in super-sonic jet...
Homework Statement
In the diagram, Disk 1 has a moment of inertia of 4.40 kg · m2 and is rotating in the counterclockwise direction with an angular speed of 7.50 rad/s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular speed of 9.50 rad/s falls...
This problem is an example from Mosca and Tipler, 9-13, 6th edition. I believe the books equation for the acceleration of the system is incorrect according to my work... Anyway, here goes
1. Homework Statement
"Two blocks are connected by a string that passes over a disk pulley of radius R...
Homework Statement
What is the moment of inertia of the 4 kg disk below when it rotates about the center of mass? The mass of the disk without the holes is 6 kg
.
Homework Equations
Center of mass equation: (1/M)(∫xdm)
Moment of inertia of a disk: I = 0.5mr2
Parallel axis theorem: I = Io +...
Homework Statement
The rods of length 2 meters and and mass 20 kg are joined at their ends to form a V shape. What is the total moment of inertia measured from the reference point perpendicular to the plane of the paper and at the point where the two rods are joined. (So find total moment of...
Homework Statement
Okay, so I'm supposed to take two fresh rolls of toilet paper and drop them. One of which, I am supposed to let unravel while falling. The other, I just drop on its own. I'm supposed to find the height at which both will drop and hit the ground at the same time.
Homework...
For a mathematics project I'm trying to figure out the moment of inertia for a propeller. I'm told that it is possible to find the moment of inertia of irregular objects through calculus, so I'm determined to figure it out using calculus.
I plan on using a 3D modelling program (since I don't...
Homework Statement
I need to find the final impact speed of the flame of a non-uniform candle. I am given that the mass per unit length increases linearly from top to bottom starting with 1kg/m at the bottom and 10kg/m at the top. I need to find how fast the candle flame is moving once the...
Homework Statement
Attached in a picture!
Homework Equations
I = mr^2
m = (x*y)
cm = (x/2, y/2)
The Attempt at a Solution
I was able to solve Part 1 fairly fast, but Part II has drawn a blank for me overall. I was thinking of that rotational thing from Calculus where you spin a 2D figure...
Starting with the orbital angular momentum of the ith element of mass, $ \vec{L}_I = \vec{r}_I \times \vec{p}_I = m_i \vec{r}_i \times \left( \omega \times \vec{r}_i\right) $, derive the inertia matrix such that
$\vec{L} =I\omega, |\vec{L} \rangle = I |\vec{\omega} \rangle $
I used a X b X c...
Homework Statement
An object rolls down a ramp starting from rest, demonstrate symbolically the calculation needed to go from time given to a measured κ value here. Pick your favourite object and perform the calculation.
d, m, R, t, h are known
http://puu.sh/luare/10352d0479.png
Soccer Ball...
Just curious, explanation if youre going to answer please!
2 horizontal disks stacked on one another spinning at constant v, (about a frictionless axis perpendicular to their center), both have mass.
Okay, so let's say its possible to instantaneously remove the top disk. So would that make...
1. The problem statementα, all variables and given/known data
The moment of inertia of a Rod over an
Axis XX' passing through the center of mass of the Rod at an angle α is-
Homework Equations
Moment of Inertia of Rod about the end, I =ML2/3
The Attempt at a Solution
I=ML2/3
Answer of the...
Homework Statement
My question doesn't follow the guidelines for asking for homework help because I'm looking for sources where I can learn about moments of inertia, not help for a specific homework problem. I'm going to try to figure out the moment of inertia of a propeller, but I don't know...
Homework Statement
Got a spicy one for you today.
There is a cylinder of mass 5kg (M) with no angular velocity and no velocity, on a surface of static friction constant μ=0.6 . It's radius is .1 meters (R). Its baricentric moment of inertia is characterized by I=.5MR^2 . Gravity is 10m/s...
Homework Statement
A thin ring of radius r is constrained to rotate with constant angular velocity ω as shown in attached picture. Let the linear mass density of the ring be ρ(θ)=ρ0(2+sin2θ) where ρ0 is constant.
a) Find the angular momentum L of the ring about O, at the instant the ring is in...
Homework Statement
A uniform sphere and a particle are sent one-by-one with the same initial speed up the same incline. Each rises to a maximum height before falling back towards the starting point. The sphere rolls without slipping; the particle slides without friction. Use conservation of...
Hi,
I'm trying to figure out the minimum power in watts or HP to move a front wheel drive vehicle that is man-powered with pedals, of a given base weight and then to know how much people would be needed to pedal in order to break inertia and a constant of how much more power is needed for each...
Homework Statement
That is the set up for experiment, and I attached the data I found in the lab.
The lab given me the equation to find the moment of inertia of the cylinder
Homework Equations
Icyl = (2hgM_cylinder) * (1/(W_withcylinder)^2 - 1/(W_nocylinder)^2)
The height is 0.9m
The Attempt at...
Homework Statement
To calculate the moment of inertia of a cantilevered tapered tube with mid-thickness large radius RL and mid-thickness small radius RS
Homework Equations
The Attempt at a Solution
Area of the larger end of the tube
AL=2*pi*RL*t
Area of the smaller end of the tube...
Hi!
I am new at robotics, can you guys please help me what is the principal moment of inertia??
how to define the pose of axis about center of mass of my robotic link of a legged robot??
please guide me with some visual representation and also how to calculate Inertia Tensor??
I will really...
hey...this is lokesh. I am really interested in automobiles but the problem is that i am a beginner. I am just not able to apply the concepts of inertia energy and torque on engines. Can you please suggest me any e-books or links which would help me clear my basics? Please reply asap. Desperate...
I have an Atwood Machine. I have an aluminium Pulley of radius 4 inch. A gym cable running over it. Not sure coefficient of friction but smooth movement. One end of rope, I attach wt. of 0.5 kg. I had to attach weight of 1 kg for acceleration to start. If I attach 2 kg, I had to attach 3.1 kg...
Hi guys,
I'm an arts undergrad student with very little knowledge of the sort of physics I'm about to ask.
I was wondering if there is a calculation to work out the differentiation between running at a particular speed say 10mph against wind coming towards you at 15mph. As well as it being on...
Homework Statement
how to divide moment of inertia of solid sphere about its central axis?. Solid sphere has radius R, mass M.
Homework Equations
I=∫r2dm
2/5 MR^2
The Attempt at a Solution
https://photos.google.com/search/_tra_/photo/AF1QipPoXyad0q1Y3yisc0LeeJHGApkIrGbitK6kAk5p
i try to...
Homework Statement
Find the moment of inertia of a spherical shell (hollow) with mass M and radius R.
Homework Equations
## I = \int r^2 dm ##
The Attempt at a Solution
This is method I use to find Moment of Inertia of solid sphere:
We use circular cross sections.
At some radius r...
Homework Statement
Is the moment of inertia matrix a tensor? Hint: the dyadic product of two vectors transforms according to the rule for second order tensors.
I is the inertia matrix
L is the angular momentum
\omega is the angular velocity
Homework Equations
The transformation rule for a...