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
What is the ratio of inertia of a 5 meter radius disk to that of a 5 meter radius ring? How would this ratio change if the ring were replaced with a since point mass a distance 5 meters from a pivot point?
Homework Equations
I = mr2
The Attempt at a Solution
The wording in...
Hi everyone,
I have just started the chapter in my Physics book that deals with calculations of Moments of momentum for various extended bodies. I have come across a problem which involves, as part of the overall problem, finding the moment of momentum of the centre of mass of the object and...
Homework Statement
Homework Equations
ml2/12
The Attempt at a Solution
So according to my databook:
The axis x'-x' in the question corresponds to axis ZZ in the databook image above. That means in terms of radius, the moment of inertia about axis x'-x' is mr2/2. So in light of this, why...
Ran into a bit of a dilemma. I'm having some problems calculating the moment of inertia for an offset weight configuration. Please see the attached drawing. Basically this offset weight will be turning around an axis as labeled in the drawing. Any help would be greatly appreciated
if i have two cylinders with same mass and radius placed over each other vertically and there is a motor inside the top cylinder welded in the cylinder itself, and connected to the bottom cylinder to rotate the bottom cylinder. assume it's the whole thing is resting on the ground and neglect...
Hello,
What could be wrong when the total inertia matrix of a robotic manipulator is non invertible when under certain values of the joint angles?
Thank you
I was thinking through a thought experiment which led me to conclude that mass is relative. My thought process was basically this; there are two objects moving past each other. In the reference frame of either object, they are at rest and the other object is moving. Since the other object is...
Homework Statement
Hello,
I know about the inertia tensor about one axis, but how about a body that rotates around 3 axis x,y and z such as a spacecraft with changes in the attitude.
Thanks for you help.
Homework EquationsThe Attempt at a Solution
Hello.
I am currently working with a beam with the following cross-section:
It consist of three bended sections with the following parameters, alpha = 90 degrees, Thickness = 4 mm, Radius = 50.59 mm.
The top section consist of a small triangle and a rectangle. the triangle have a width = 4 mm...
Homework Statement
A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices.
Homework Equations
Slender rod, axis...
Homework Statement
Homework Equations
...
The Attempt at a Solution
I've been searching for the relation between the spinning speed and inertia in equation form. I do know that since the skater inertia is smaller the spinning speed is faster but that about it. Any hint would be helpful. One...
I need to make a project that integrates physics with math, involving the use of integrals to find moment inertia of areas. The theory could be read here :http://www.intmath.com/applications-integration/6-moments-inertia.php
I need to make an object that applies the theory above. Can anybody...
Homework Statement
A slender rod is 80.0 cm long and has mass 0.120 kg. A small 0.0200-kg sphere is welded to one end of the rod, and a small 0.0500-kg sphere is welded to the other end. The rod, pivoting about a stationary, frictionless axis at its center, is held horizontal and released from...
1. A 3.0 kg vertical rod has a length of 80 cm. A 4.0 kg rectangle attached to the top of the rod has negligible dimensions. The entire object rotates counterclockwise about the bottom of the rod. Determine the angular speed of the apparatus at the instant the rod is horizontal.
2. Using...
Is there an equation for the moment of inertia of a propeller? If so, what is it? If there isn't one, can I use the moment of inertia of a rectangular slab? Thank you in advance.
Hi,
I wonder if a gravitationally bound system ...like a binary star system (or a spinning galaxy for that matter) has a similar inertia in its rotational axis like your classic spinning top? Is there resistance to a change in the axis?
I appreciate the system is not solid and so not obviously...
Homework Statement
A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR^2. A light string of length 3R is attached to the surface and used to suspend the sphere from the ceiling. What is its rotational inertia about the point of...
Homework Statement
A given pulley has a radius of 20 cm and moment of inertia 0.2 kgm2. The string going over it is attached to a vertical spring of spring constant 50 N/m on one end and a 1 kg mass on the other end. The system is released from rest with the spring at natural length. Find the...
Homework Statement
Why is it that when you integrate to find the moment of inertia of a cone standing on its vertex (like a spinning top) with height h mass M and radius R do you integrate the R limits as 0 to (R/h)z in the triple integral (cylindrical coordinates) below?
Homework Equations
I =...
Homework Statement
The shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.0000 m and (total) mass M = 100.0 mg. The disks are uniform, and the disk arrangement can rotate about a perpendicular axis through its central disk at point O...
Homework Statement
Question is provided
The Attempt at a Solution
The required solution is provided
My question is, the examiner have used sine theta in their expression for change in potential. I keep ending up with 1 - cosine theta
Second question is how did they get rid of theta in the...
Homework Statement
The horizontal side (x-axis) is length 2A and the vertical side (y-axis at x=+-A) is length B. The mass is uniform throughout the sheet so that the center of mass is at the center of the rectangle. What is the moment of inertia for. the rotation around the z-axis at the...
Homework Statement
A uniform spherical ball of mass M and radius R, initially spinning about a horizontal axis with angular speed ω0, is placed gently on the floor. The initial center-of-mass velocity of the ball is zero. Derive that the moment of inertia ICM of the ball about an axis passing...
1. Homework Statement
a circular homogenic pulley (disk) with radius R and mass of M hanging on a axis that passes through his center,
the pulley rotating without friction.
we wrap the pulley with a rope with a total mass of mr and length of L and in the other side of the rope we ataching...
Homework Statement
Prove the formula for inertia of a ring (2D circle) about its central axis.
Homework Equations
I = MR^2
Where:
M: total mass of the ring
R: radius of the ring
The Attempt at a Solution
- So I need to prove the formula above.
- First, I divide the ring into 4...
If a bullet were to strike the Earth at a velocity close enough to c that its relativistic mass approached that of the Earth, would the damage be equivalent to that of an object of similar invariant mass colliding at a non-relativistic velocity? (The reason I ask is that in Liu Cixin's sci-fi...
I was wondering why the head has it's own inertia during whiplash when the person is rear ended by another car?
I thought that the head would be moving forward also because it is part of the system of the chair being impacted to move forward?
I know most of the formula's but I'm trying to get a conceptual understanding of everything and finding it very hard to get concise information about everything all in one place especially when there are so many names for the same thing. Most resources just rehash the formulas without explaining...
Homework Statement
Determine the moment of inertia of a rigid body on the picture:
The radius of the inner cylinder is R and the outer is 2R.
Homework Equations
3. The Attempt at a Solution [/B]
I thought of subtracting the big cylinder inertia from the small and adding the hanging body and...
Homework Statement
Find the period of small oscillation of this system.
Homework Equations
3. The Attempt at a Solution
[/B]
I understand the concept of moment of inertia but can't comprehend the first equaion here. The other two i get and they are moments of inertia of other two bodies...
Homework Statement
I'm reading a paper and I'm trying to understand how does the author arrived from equation (1) to the following buckling load equation (2). I know that the author substitutes equation (1) with the dimensions of the geometry but I still could not understand how he comes to...
Homework Statement
The uniform beam shown in the IMAGE below has a weight W. If it is originally resting while supported on A and B by cables, determine the pull on cable A if cable B suddenly fails. Admit that the beam is a slender rod.
IMAGE:
Homework Equations
TotalTorque=I*α...
Homework Statement
If we multiply all the design dimensions of an object by a scaling factor (f), its volume and mass will be multiplied by f^3. a) By what factor will its moment of inertia be multiplied? b) IF a 1/48 scale model has rotational kinetic energy of 2.5 Joules, what will be the...
Homework Statement
There is a steamroller with total mass 12000 kg on a 4° slope. It has 2 wheels (full homogeneous cylinders) with mass 3000 kg (each one 3000 kg) and diameter 1,2 m (radius 0,6 m). How big would the acceleration of the steamroller be if brakes got broken.
Result: 0.56 m/s^2...
Why heavy cars took more time to stop than lighter cars to stop when braking ??
Is it related by Inertia , if yes then why it's related by Inertia because i don't understand the physical concept of inertia
I need help to prove that the moment of inertia of a uniform square of mass m and side d about an axis through its centre, parallel to a side is 1/12 md²
1. The problem statement, all variables and given/known
See attachment , it only gives me length of rod and it's mass and radius of sphere and its mass and the place of the axis
Homework Equations
I=mr^2
The Attempt at a Solution
I tried to get the moment of intertia of rod by integration from...
question 1 The vector field F(x, y, z) = 2xi + 2yey2+z j +(ey2+z + cos z) k is conservative. Find a
corresponding potential function.
* e raise to power (Y square +z)
Question 2
Consider a solid sphere of radius R, a cylindrical shell of outer radius R, inner radius a,
and height h, and a...
I often hear inertia used as an explanation in areas where it seems to make intuitive sense, but appears to me to be inconsistent with the definition of inertia as just depending on an object's mass. I offer three examples (they're very similar):
Example 1: An elevator
Suppose an elevator...
Hi
Have a look at attached formula. This is a part of a software. it is 'Inertia' which has 'Kg.m^2' unit.
You know 'Kg.m^2' is 'Moment of Inertia' unit. What is your idea about this? Does it use 'Inertia' as 'Moment of Inertia'?
Homework Statement
Consider a circular disc (that might be a tautology), free to rotate and translate in the xy-plane only. It has radius R, but its mass is unhomogeneously distributed in some unknown fashion. All we know is that the center of mass is displaced from the centre of the disc by...
Use a parallel axis theorem to determine the moment of inertia of a uniform disc of mass M and radius R about the x-axis perpendicular to the plane of the disc and passing at the edge of the disc.
Homework Statement
A small pine tree has a mass of 15kg. Its center of mass is located at .72m from the ground. Its trunk is sawed through at ground level, causing the tree to fall, with the severed trunk acting as the pivot point. At the instant the falling tree makes a 17° angle with the...
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...