Inertia Definition and 1000 Threads

So I have been having a bit of trouble trying to derive the moment of inertia of a solid sphere through its center of mass. Here is my working as shown in the attached file. The problem is, I end up getting a solution of I = (3/5)MR^2, whereas, in any textbook, it says that the inertia should...

Homework Statement Moment of inertia of a metal plate (center at origin) which was a square before 1/4th of it was cut off (4th quadrant), about three points a)- top leftmost corner in 2nd quadrant b)- origin and c) (where the right-lowest corner used to be in 4th quadrant) ranked in decreasing...

Homework Statement Three slim rods with the same length L are placed in a inverted U shape, as the figure shows. The masses of the vertical rods are the same, while the third bar has the mass 3 times bigger than the first or the second rod. The rods' thickness should be ignored. Find the moment...

Calculating for a section of an engines connecting rod that is always changing speed I have seen different formulas for inertia. Must be different types. Since it is changing speed I guess I am looking for the inertia that is against that change. any help is much appreciated. I know ya'll get a...

Hi PF! The capillary number is defined as ##Ca = \mu V/\sigma##. Does more inertia in a fluid increase the capillary number? As inertia increases, it's my intuition that so does velocity. Then it seems (all else constant) that ##Ca## increases too. Is this correct?

Is there any way to approach to some kind of explanation for inertia,from higgs field?

Good day! How do I calculate how much torque I need in a motor for my project? I must rotate a 100lb propellor, which is 11 ft in diameter, at 1 rpm .

Homework Statement :[/B] A uniform wire of linear mass density λ having three sides each of length 2a is kept on a smooth horizontal surface. An impulse J is applied at one end as shown in the figure. P is the midpoint of AB. Now answer the following questions. 1) The angular velocity of system...

Homework Statement 1. Homework Statement An uniform disk of mass m, thickness L and radius r is suspended from the ceiling by a wire. It is attached to the disk at a distance, d from the center of mass, so that it inclines at an angle A to the vertical. What is the moment of inertia of the...

Hello everyone. This is my first time on the physics forum, but I think I'm going to be a regular here. I was reading a paper that outlined various ways to approach solving dynamic problems. The first approach outlined by the author is D'Alembert's principle of virtual work. In describing...

Homework Statement Find moment of inertia of a washer with a hole of radius r/2. Homework Equations Moment of inertia = integral of x^2 dm γ = m / L The Attempt at a Solution I think I can find the moment of inertia of the washer using integral of x^2 dm. So, I know my γ = m / L = m /...

Homework Statement The moment of inertia about an axis through the center of mass of a system consisting of two masses 3.0 and 5.0 kg connected by a rod of negligible mass 0.8m long is Homework Equations [/B] I = I1 + I2 The Attempt at a Solution I added all the moments of inertia of the...

Homework Statement A meter stick has a mass of 0.2kg. A small hole is bored in it at the 10cm mark so the meter stick can be hung from a horizontal nail. The moment of inertia of the meter stick around an axis at the 10cm mark is Homework Equations m = 0.2kg I = mr^2 The Attempt at a...

Homework Statement The picture illustrates a simple pendulum and and two physical pendulums ,all having the same length ,L. Class their period in ascending order. Homework Equations T = 2π / ( I/mgh) I = Icm + mh2 Icm=(ML2/12) The Attempt at a Solution I have found the period for first...

Homework Statement Consider a half disk (of uniform density) with the flat end lying on the x-axis, symmetric about the y-axis (i.e. being cut into two quarters by the y-axis). Calculate the moments of inertia about each of the axes. Homework Equations $$I_{rr}=\sum_{i}m_ir_i^2$$ The Attempt...

Homework Statement Assume the balance wheel of a torisonal pendulumn is doubled in size but the torison constant of the spring remains the same. The density of the disk remains the same, but bot the radius and the thickness double. What happens to the period of the pendulumn? a) Period doubles...

Homework Statement I'm trying to figure out the mass moments of inertia for a hexagonal prism, with the z-axis being longitudinal. I'm trying to recall my calc 3 from 2 years ago and am failing miserably. I know the height of the prism is h. Each hexagonal side is length a. The prism has...

Hello! The equation for relativistic mass by special relativity tells us the relativistic mass for object in motion...but since inertia mass has same value as gravitational, does this formula also apply for gravitational mass? Thank you!

Homework Statement Homework Equations I=1/12*bh^2+Md^2 The Attempt at a Solution for the highlighted 600mm^2 (and the 300mm^2 below) in the middle of the page, when finding the moment of inertia, what the solution used is an area, yet for related formula required the use as for mass in the...

Homework Statement Find the 2 unknown variables.[/B]Homework Equations Am I doing this right? Can someone help me find the solution?[/B] The Attempt at a Solution To compute for the velocity of the target/arrow combination immediately after the collision: M_bV_{bi}=M_bV_{bf}+M_wV_{wf}...

I have my students doing a lab where they have to do and explain the tablecloth trick using Newton’s Laws. The problem I am having is that the one question asks why the quick removal of the tablecloth matters. I know friction is not affected by speed and yet this is the only force acting on the...

I've read other posts about this but I don't think this question was covered. Say you have two objects with different masses in a vacuum sitting on some kind of plank. Next, you remove the plank from both at the same time. The heavier object has a greater inertia, which means that it has a...

Homework Statement Homework Equations inertia equations The Attempt at a Solution I think the answer for this is B) or D) but I am not sure what the sentence "a special solid cylinder in which the density is proportional to the radius" means... The solid sphere has little inertia because...

Homework Statement Two planets are masses stuck to end of long thin rods. These model systems (Rod + mass) will be rotated by a motor at their other end of the rod, as shown in the figure. the length of the rod is proportional to the orbital distance of the planet, and the mass at the end is...

Homework Statement Homework Equations I = mr^2 (point mass) The Attempt at a Solution I wasn't sure how to calculate the moment of inertia of this triangle if the axis is going through one vertice perpendicularly. Do i calculate the inerta of 2 sides with Inertia of a rod and the 3 side as...

Hi there. I have a question about the tuning of a PID (PI) controller in hydraulic drive trains with high inertia. I have a system with a 100kW hydraulic motor with an installed on its shaft encoder. That is how I am getting feedback from it. Not surprisingly I have a controller for acquisition...

Homework Statement When a disk rolls in a surface whitout slip, the velocity of the disk's edge (where it contacts the surface) is zero with respect the surface and the friction force is less than the maximum allowable of Us.N, where Us is the coefficient of static friction and N is the normal...

Hello, this formula was given to me in an exam to find the moment of inertia of an I beam, https://ibb.co/jY7ZKG However this formula seems to give a different answer to the standard bd^3/12 method, is the formula in the image wrong ? Thanks

Homework Statement A thin stick of mass M = 3.9 kg and length L = 1.8 m is hinged at the top. A piece of clay, mass m = 0.3 kg and velocity V = 2.9 m/s hits the stick a distance x = 1.60 m from the hinge and sticks to it. What is the angular velocity of the stick immediately after the...

Homework Statement Consider a hollow cylinder of mass M with an outer radius R_out = 10 cm and an unknown inner radius R_in. If the hollow cylinder is to roll down an incline in the same time as a spherical shell of the same mass and the same outer radius, calculate R_in. Homework Equations...

<<<moved from another sub forum, no template>>Hi, I need to calculate the moment of inertia for the component in the attached image so that i can calculate the angular momentum. Is it possible? Overall i am trying to calculate the forces on this lug as it passes around a 3" radius at 2M a...

In the picture the question marked spot is confusing me. Should the MI be calculated in this ugly way? That we do not consider the points in between and on dx! Why only x is taken as the distance? You may say take x+dx, resulting dx in the exapnsion and the dx from the mass to square and being...

Now, if I am not mistaken, a gymnast can rotate around his or her axis while spinning, and they can speed up and slow down their speed of rotation by changing the radius part of their moment of inertia; you know, extending legs and arms outward or bringing them inward. I want to know, however...

Homework Statement I was learning how to calculate moment of inertia on Youtube, and I'm confused about when to use 1/2 mr2 instead of mr2. This video says that he used 1/2 mr2 instead of mr2 because the cone is solid But in this video, while he was calculating a solid sphere, he used mr2...

Hi, in the following problem, I need to find the inertia of the system. The axis of rotation passes through the center of mass ( the pink dot). I understand that I will be equal to 4(mr^2). However, I do not understand why r= 3 (6 divided by 2) and not sqrt13 ( half of the diagonal of the...

Homework Statement Kindly see the screenshot attached below for the question. Homework Equations I=1/3ML^2 1/12ML^2 The Attempt at a Solution In the solution to this question, the moment of inertia of the hands (when outstretched) is taken to be 1/12ML^2 (combined). I think that it should be...

If two gears are joined to together, how are their moment of inertia calculated? Separately or combined?

Homework Statement A space station (moment of inertia 5,000,000 kg•m2) is rotating with angular speed 0.30 rad/s when the 10 inhabitants are in the outer ring (radius 100 m). One half of the inhabitants move to the inner ring (radius 50 m). The average mass of each inhabitant is 70 kg. a...

I was reading this article Why Einstein did not believe that general relativity geometrizes gravity and it seemed rather interesting. So it would be interesting to hear what others think of it. It suggests that Einstein's view on GR was that it does not reduce gravity to inertia and geometry...

Homework Statement A disk of radius R has an initial mass M. Then a hole of radius (1/4) is drilled, with its edge at the disk center. Find the new rotational inertia about the central axis. Hint: Find the rotational inertia of the missing piece, and subtract it from that of the whole disk...

Homework Statement You decide to design a bicycle that will have only 3/4 of the angular momentum of the original wheel when both wheels are traveling along a road at the same velocity. The original wheel had a diameter of d1=37cm and rotational inertia of I1=0.32 m2kg. If your new wheel has a...

Homework Statement The object is made out of multiple parts. The inertia matrices of every part are given. Only one part is rotating. How do I find the total inertia matrix. Homework EquationsThe Attempt at a Solution I thought that I could sum the inertia matrices, after tranforming them to...

Homework Statement Okay, so this isn't so much a problem as a design issue while following an example given in a book. (Relevant material is here: http://www.aero.us.es/adesign/Slides/Extra/Stability/Design_Control_Surface/Chapter%2012.%20Desig%20of%20Control%20Surfaces%20(Elevator).pdf ) Now...

Homework Statement A car accelerates from rest on a horizontal surface. The engine provides a torque of τ = 200 Nm on each of the two front wheels. Each of the four wheels on the car weigh m = 15 kg, have radius R = 0.35 m and can be considered solid, uniform discs. The rest of the car (not the...

A girl is climbing up a set of stairs and has her femur horizontal. Her thigh weighs 12 pounds, acting at a center of mass 15 cm from her hip joint. She places 50 pounds of weight on the lower portion of that leg, vertically through her knee. Her gluteus maximus is applying a force directed 30...

Homework Statement A disk with a rotational inertia of 8.38 kg·m2 rotates like a merry-go-round while undergoing a torque given by τ = (5.03 + 1.01t) N · m. At time t = 1.00 s, its angular momentum is 6.57 kg·m2/s. What is its angular momentum at t = 3.00 s? Homework Equations dL/dt= T...

Hi I am struggling with the following question. A cylinder of radius 20cm is mounted on a horizontal axle coincident with its axis and is free to rotate. A light chord is wound onto it and a 50g mass hung from it. After release the mass drops 1m in 12seconds. What is the moment of inertia...

Homework Statement Calculate the moment of inertia in the OO' axis of the following figure (image attached).Homework Equations The relevant equations are in the image, except: I = Icm + m.h2 (formula of moment of inertia to change the axis from the centre of mass to a parallel axis). The...

(Forgive me if this is in the wrong spot) I understand how tensors transform. I can easily type a rule with the differentials of coordinates, say for strain. I also know that the moment of inertia is a tensor. But I cannot see how it transforms as does the standard rules of covariant...

Explain the phenomenon of closing of door of a car when car starts accelerating forward please explain in ground frame.