Inertia Definition and 1000 Threads

Okay, so the scenario is a passenger car, traveling on the highway. As a general rule, I say that increased weight (mass) will have a beneficial effect on MPG (IF tire pressure is increased so that rolling resistance is reduced to compensate for the increased weight), ONCE the vehicle is up to...

Homework Statement A solid wood door 1m wide and 2m high is hinged along one side and has a total mass of 40kg. Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass .5kg. What is the original and final moment of inertia for the door? What is the...

Homework Statement Find the moment of inertia of a rectangular plate of mass m, sides 2h and 2k , rotates about its diagonal. Homework Equations I= Ʃmr^2 The Attempt at a Solution I=Ʃ m(x^2 +y^2) , let 2h parallel to x-axis, 2k parallel to y-axis. I= m(x cosθ)^2 + m (y cos ∅)^2 where...

Homework Statement Four T-shaped objects are constructed by connecting two identical rods of equal mass and equal length. Rank in order, from LARGEST to SMALLEST, the moments of inertia for rotation about the axis indicated by the dashed line. Homework Equations The Attempt at a...

Homework Statement A uniform square plate ABCD has mass 0.8 kg and side length .8 m. The square is pivoted at vertex D and initially held at rest so that sides AB and CD are horizontal (see the diagram). After it is released, the plate swings downward, rotating about the pivot point...

Homework Statement A cylinder with radius R and mass M has density that increases linearly with distance r from the cylinder axis, ρ = αr, where α is a positive constant. Calculate the moment of inertia of the cylinder about a longitudinal axis through its center in terms of M and R. This is...

Hello, I'm working on a generalized model for motor / gear systems in SPICE and came across something I don't understand: Given that the inertia, J, is in kg m^2 and my base unit for angular velocity, w, is kRPM and the basic equation for energy is E = 1/2 J * w^2 How or what is the...

Homework Statement If we multiply all of the design dimensions by a scaling factor f, it's volume and mass will be multiplied by f^3. (a) By what factor will its moment of inertia be multiplied? (b) And if a 1/48 scale model has a rotational kinetic energy of 2.5J, what will be the kinetic...

Hi everyone. I'm presently improving a 2D physics engine i wrote, with angular dynamics. Moment of inertia is becoming a big sticking point for me. However, given that my applications are fairly simple, I'm hoping someone can help me come up with a simple way of calculating the moment of...

Homework Statement There are four masses (particles) with a mass of 30gr each and they are at the vertices of a square that has each side with a length of 90cm. What is the moment of inertia of this system through a perpendicular axis that is at the center of the square?The Attempt at a...

Homework Statement A dumbbell has two spheres of radius 0.10m and mass 10kg (each). The two spheres are connected using a bar with length 1.0m and mass 12kg. What is the moment of inertia of the dumbbell about an axis perpendicular to an axis at the bar's center of mass? Moment of inertia...

Hello, I am trying to find moment of inertia of various random 3D shapes and I have few general questions. I take very thin 'plates' of the shape, calculate moment of inertia of that area, multiply it by thickness of one 'plate unit', also I add a square distance it is from the origin...

Hello everybody! This is the derivation (for a single particle). \tau = F_{\perp }r \ = ma_{\perp}r \ = \alpha mr^2 \\ \text{if }\ \tau = I\alpha \text{ where } I \text{ is resistance to accleration then } \\ I = mr^2 I'm curious what the problem with this is because I haven't...

Hi there, I am trying to calculate both volume and moment of inertia of shapes which surface coordinates are depicted by following equation: |xn| + |yn| + |zn| = Rn When n is 1 it is simple octahedron, when it is 2, it is sphere and then choosing any n, it becomes something else. I...

Minimizing the Moment of Inertia while keeping the Moment constant Hi there. I am dealing with a mathematical problem which seems to be much harder than I initially expected: Minimize the functional J(\Omega) = \frac{1}{\rho} I_{z} = \int \!\! \int \!\! \int_\Omega \left( x^{2} + y^{2}...

Hi, I read in a textbook that area Moment of Inertia (M.I.) of any shape would be Ʃ of (y2 χ A)1,2...n where, A represents the Area of strip no. 1, 2... n y is the distance between globlal centre of gravity (C.G.) of the shape to th local C.G. of strip no. 1, 2... n (pl. look at the image)...

Homework Statement Square lamina (of side a) of uniform density. Find I about a diagonal. Homework Equations I = ∫ dm*l^2 The Attempt at a Solution So I drew a square and its diagonal and I imagine a differential mass drawn somewhere on the lamina. The distance squared to that...

Homework Statement A rod is 10 ft long and has a density that goes from 4 to 24 lb/ft. a) Find the mass. b) Find the center of mass. c) Find the moment of inertia through the center of mass. Homework Equations I = Ml^2 I = I(cm) + Md^2 (parallel axis theorem) The Attempt at...

Homework Statement An oxygen molecule consists of two oxygen atoms whose total mass is 5.3x10^-26 kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is 1.9 x 10^-46 kg*m^2. From this data, estimate the effective distance between...

How do physicists determine whether the thing they are measuring, a particle for example, is inert or under motion?

Homework Statement Find angular acceleration in deg/sec^2 given the following factors: - Total mass: 4889 kg - Moment of inertia: 4620 kg*m^2 - Moment arm length from center of mass: 1.5 meters - Force on moment arm tangent to mass: 1779 Newtons Homework Equations torque = force...

Hi everyone, Is there a general method for finding out the moment of inertia of an irregular convex 2D polygon given the coordinates of its vertices? I have thought of one possible method: Split the polygon into multiple triangles and find the moment of inertia of each triangle around the...

Why can't moment of Inertia be never greater than MR2 for uniform bodies with simple geometrical shapes?

The Coin(Green) in lying on a paper which is lying on a box.When I pull the paper with a higher force so that I could remove it easily,the coins stays about the same place. When I remove the paper slowly,the coin comes with the paper. Why? I think that objects can react(Move) to smaller...

Hi, I've attached a word document with my problem since I've used the Mathtype program (sorry, I didn't quite know how to use the tools on this forum), hope you don't mind :)

Box B sits on top of box A. IF we apply a force to box A and cause it to move to the right; then box B moves to the left. Why? Why doesn't box B also move to the right? Can someone explain this? I keep doing such experiments but can't figure it out.

Dear all, correct my understanding... Inertia should be applicable at sub atomic level as well. right ? Consider this scenario, a positively charged helium ion is accelerating. the electron cloud in this case should be somewhat oval or elliptical right ? this would be because, the...

Homework Statement A hoop with mass m= 10 kg, radius r=0.6 m, and moment of inertia I=mr^2 is rolling without slipping with a linear velocity of 8.5 m/s. What is the total kinetic energy (in J). Homework Equations K=1/2 m v^2 Kr=1/2 I ω^2 The Attempt at a Solution The kinetic...

Regarding the moment of inertia constant, k, as in I = kmr^2, k is often a fraction less than one, and sometimes is equal to one. http://en.wikipedia.org/wiki/List_of_moments_of_inertia Is there an example of k being greater than one?

A 60kg skater begins a spin with an angular speed of 6.0 rad/s. By changing the position of her arms, the skater decreases her moment of inertia by 50%. What is the skater's final angular speed? I(initial)ω(initial) = I(final)ω(final) I used 60 kg as my inertia, is inertia and mass...

Homework Statement How do you calculate the moment of inertia of a regular hexagonal plate of side a and mass M along an axis passing through its opposite vertices?Homework Equations Moment of inertia for a right triangle with an axis running along its base would be I = m h2 /6 where h and m...

How does momentum and inertia affect changes in speed, when considering acceleration from thrust, or from decelleration from drag? Say, for a fixed mass of 100kg, at a velocity of 10m/s, is a force of 10N is applied in the forwards direction, then F = ma -> a = F/m. a = 10/100, a = 0.1 m/s^2...

hello! I have to verify the formula of the moment of inertia of an ellipse about its' centroidal axis, is it M*(a^2 + b^2)/4.This is the one I got by myself. But in a webpage it was given as Pi*a*(b^3)/4. NOTE: don't ask for the proof of what I did.Its' a bit longer.I just want to know...

Homework Statement What must the ratio of height to radius of a cylinder be so that every axis is a principal axis (with the CM as the origin)? Homework Equations Moment of inertia tensor. I need I_yy = \sum m *(x^2 + z^2) The Attempt at a Solution I calculated I_zz = MR^2 /12...

Homework Statement A 4.00-m length of light nylon cord is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.00 kg. The spool is mounted on a frictionless axle and is initially at rest. The cord is pulled from the spool with a constant acceleration of magnitude 2.82 m/s2...

Homework Statement Two concentric disks are welded together with a small hole through the center. This two disk unit is mounted onto a frictionless horizontal axle through the center hole. Two strings are attached and wound in opposite directions around the outer perimeter of each disk and...

Okay, we have one-thousand pounds; at sea level, and a feather. We elevate them to a thousand meters and support them on a platform. All of which is in a vacuum. We remove the platform, they both hit the earth; the limiting surface; at the same time. Newton's second law suggests that this is due...

Homework Statement The two small spheres of mass m each are connected by the light rigid rod which lies in the x-z plane. Determine the mass moments of inertia of the assembly about the x, y, z axes. I have attached an image of the question Homework Equations The Attempt at a...

Hi, I'm new here and didn't really know where to put this so decided to put it here as it is to do with my course work. I'm currently doing my Final year project on a lifter for lifting fertilizer bags its going okay and do know how to calculate moment of inertia but the problem is that I have...

Homework Statement Determine the angular acceleration of the uniform disk if (a) the rotational inertia of the disk is ignored and (b) the inertia of the disk is considered. The system is released from rest, the cord does not slip on the disk, and bearing friction at O may be neglected. The...

Homework Statement a)Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page. In kg m^2 b)Find the moment of inertia about an axis that passes through masses B and C.In kg m^2 http://session.masteringphysics.com/problemAsset/1070524/4/12.EX16.jpg...

My workings are below : Following the calculation of w I use v=wr where r= 3 and calculate the tangential velocity. It's then easy to see that a speed of 340 (Mach 1) will be attained in 128 s Is this correct ?

how could i calculate the moment of inertia of a tyre if i needed the moment of inertia about the central access of the tyre could i add the moment of inertia of the tyre+ the moment of inertia of the rim and how do i calculate the moment of inertia of the tyre, i can't find any assosiated...

what is the moment of inertia about the wheels , when the vehicle is accelerated upto 100 km/hr and the foot is lifted off the accelerator

I have been scratching my head for a few hours now. Problem is I don't believe my calculations one bit haha. I have a circlular rotating disc mass (approx 80Lbs) radius of 13" I have 16 Blades evenly spaced on this mass(approx weight of 3.2Lbs/each) Inside radius is 13" outside radius is...

hi all, This is a question regarding calculation of effort required to over come the inertia of a body.Let us have a ring(Some random example) which is supported by three rollers(Ring is sitting on the rollers).To rotate the ring,the applied effort has to overcome the friction and inertia of...

Homework Statement Given: A flat dance floor of dimensions lx = 17mbyly =15mandhasamassofM = 1100 kg. Use the bottom left corner of the dance floor as the origin. Three dance couples, each of mass m = 100 kg start in the top left, top right, and bottom left corners. What is the initial y...

Homework Statement In the image attached, I'm asked to find the mass moment of inertia about an axis at point O that's perpendicular to the page. The Attempt at a Solution The only question about this problem that I have is: Can I divide the composite body at point O and find the...

Homework Statement A drink can is placed on a rough-surfaced, stationary conveyor belt of a supermarket checkout. The can is modeled as a cylinder consisting of two equal discs, each of mass m1 and radius R, that are the top and bottom, and a curved surface of mass m2, radius R and length h...

a vehicle is moving at 100 km/hr. the foot is lifted off the accelerator, and the vehicle decelerates, if a mechanism is introduced to absorb the toque from the differential gear(bevel ring gear). and it decelerates the vehicle from 100 km/hr to 50 km/hr. what would be the amount of torque...