Inertia Definition and 1000 Threads

The moment of inertia of a rod with consistent density rotating about its end is M(L^2)/3. However, if you treat the rod as a point mass and try to calculate this using mr^2, you get M(L/2)^2=M(L^2)/4. Why doesn't this work?

Homework Statement (a) Consider a cylindrical can of gas with radius R and height H rotating about its longitudinal axis. The rotation causes the density of the gas, η, to obey the differential equation dη(ρ)/dp = κ ω2 ρ η(ρ) where ρ is the distance from the longitudinal axis, the constant κ...

Hello, I need to measure the moment of inertia of a DC motor's rotor. Any suggestion? Thanks

Hi, I need some assistance understanding moments of inertia. I am doing some review for an upcoming exam, however I am slightly stumped by this question. I have already tried googling "moments of inertia" to try and understand the concept better, but I am having issues knowing when to apply...

Homework Statement Compute the moment of intertia Io of the two cylinders, per their axis of symmetry, and then, using Steiner's formula, the moment of inertia Ib, as per the axis of rotation. Homework Equations Io = 1/2*m*R2 Ib = 2*(Io + m*x2) The Attempt at a Solution Now, this is...

So i was going through derivations of moments of inertia of objects. For objects like the disk and rod, i was able to assume a relationship between mass and volume and integrate From there like $$ \frac{d_m}{m} = \frac{dl}{l} \\ d_m = \frac{dl*m}{l} \\ \int_{0}^{L}r^2\frac{dl*m}{l} \\...

i know how to calculate the inersia for the cylinder, than i have to take away the inersia of the rectangel, but i can't find an equation for the inersia for a rectangel with the plane spinning perpendicular to the rotation axis, please help !

A 24 kg solid door is 220 cm tall, 95 cm wide. What is the door's moment of inertia for rotation about a vertical axis inside the door, 17 cm from one edge? I've looked at examples of how to do this problem. They connect it to center mass but I get confused when determining what the center mass...

Do elementary particles have inertial mass in the same way composite objects have? If yes, does it have an impact on the motion or on the forces that act on them?

Homework Statement To calculate moment of inertia of a solid sphere of uniform density[/B]Homework Equations $$ I = \int r^2 dm$$ The attempt at a solution I consider an elemental disk of small thickness ##d\theta## ##dm = \frac{M}{4/3 \pi R^3}*\pi R^2\cos^2\theta* Rd\theta##...

Homework Statement Three equal point masses, mass M, are located at (a,0,0), (0, a, 2a) and (0, 2a, a). Find the centre of mass for this system. Use symmetry to determine the principle axes of the system and hence find the inertia tensor through the centre of mass. (based on Hand and Finch...

Homework Statement A non uniform disc of radius R has a mass of M. Its centre of gravity is located at a distance x from the centre. Find the moment of inertia of mass (moi) around the axis perpendicular to the surface passinf through the centre of gravity. Homework Equations Parallel axis...

Good evening, good people of PF. I have a fairly simple question. Please see the attached drawing. My question is this: does the moment of inertia change from position one to position two (as the weight is rotating around a center line). In essence, does it maintain the same moment of inertia...

I know it's possible to use a trifilar pendulum to extract information on moments of inertia by measuring the period of oscillation. I've seen this test being executed on small aircraft, like in this video. But I wonder how do is the momement of inertia calculated on big aircraft, like a Boeing...

Homework Statement The question is uploaded. Value of g = ## \small \rm 10~ms^{-2}## Inertia of the individual square lamina = ## \rm \small \frac{1}{12}mr^2 ~kgm^{2}## The Attempt at a Solution $$\ C=Ia$$ $$\ Moment~of~Weight~of~Particle=1.594a$$ $$\ 0.3*2g=1.594a$$ $$\ 6=1.594a$$ $$\...

Homework Statement A 45 RPM record is a disk with a wide hole in the center. The mass of such record is 45g. It is 7 inches in diameter, and the hole in the center has a 1.5 inch diameter. (Sorry for the odd units, this was the way it was given). Find the moment of inertia of the 45 RPM...

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...

Hi, I couldn't find how to calculate this flywheel inertia , any help please?! I know that I=1/2(mass*radius²) but it seams more complex then that!

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...