Inertia Definition and 1000 Threads

Find moment of inertia of a uniform quarter disc of radius R and mass M about an axis through its centre of mass and perpendicular to its plane ... I tried in the following way: I considered the relation. I= Icm + Md2 Where d is the distance between required axis and centre of...

it is involved the concept of inertia ?? when a plane is flying on the sky , sometimes it will remain the constant velocity,right?and the force is balanced therefore , it does not have any force? why the plane can keep moving at the constant velocity ? due to inertia ? :confused::confused:

Homework Statement To calculate I, the moment of inertia of an ellipse of mass m. The radius are a and b, according to the drawing. Homework Equations I=mr^2 Ellipse: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \Rightarrow y=b\sqrt{1-\frac{x^2}{a^2}} Area of an ellipse: \piab The Attempt at a...

Hello everyone, I am trying to solve some homework but I am not entirely sure what formulas to use. Problem) There are 3 kids that weigh 25kg each sitting in the center of a merry go round (Disk). The merry-go-round weighs 400 kg and has a diameter of 3 m. It is initially spinning at 50 rpm...

So I have a question. I (moment of inertia) is basically mr^2 right? And r is supposed to be the distance from the axis of rotation. When the axis of rotation is directly through the center of mass, how is there Icm (moment of inertia about the center of mass). It's confusing to me, because so...

Homework Statement Calculate the moments of inertia I_1, I_2, and I_3 for a homogeneous cone of mass M whose height is h and whose base has a radius R. Choose the x_3 axis along the axis of symmetry of the cone. Choose the origin at the apex of the cone, and calculate the elements of the...

Homework Statement A beam of mass m and length L with a moment of inertia (mL^2)/12 carries additional masses of m/2 at one end and at its centre. The moment of inertia about its centre is now... (a) - (5/24)mL^2 (b) - 0 (c) - (1/12)mL^2 (d) - (1/3)mL^2 (e) - (17/96)L^2 Homework...

Homework Statement I need to derive the moment of inertia of a thin rod with its axis of rotation at the end of the rod. http://en.wikipedia.org/wiki/List_of_moments_of_inertia The third one. Homework Equations I = mr^2 The Attempt at a Solution I completely understand how the...

Twelve uniform, thin rods of mass and length are welded together to form a “wheel” as shown in the figure. What is the moment of inertia of this wheel for rotation around an axis through its center and perpendicular to the plane of the wheel? The welds contribute no mass to the wheel. I...

Homework Statement Homework Equations The Attempt at a Solution For part B, why is he using the formula for the moment of inertia about the y-axis? Why isn't he using the formula for the moment of inertia about the origin...

I got one multiple choice on our exam incorrect, and I was wondering exactly why this answer is correct: When you accelerate your car, the front of the car lifts up slightly. Or when you brake, the front dips down. The primary reason is because the A) center of mass of the car and its...

Homework Statement Consider a cuboid of lengths a, b and c along the x, y and z axes respectively, centred at the origin. The task is to show that the moment of inertia of the cuboid of mass M and mass density ρ about an axis along the body diagonal, from (-a/2, -b/2, -c/2) to (a/2...

In a recent physics class I took, my teacher explained how friction is not affected by surface area, but by the "bumpiness" of the two objects and the mass, as well as other things, but not the surface area. But this made me wonder how nails get harder to pull out the deeper they are embedded in...

Homework Statement For any flat object, located in the x-y plan applies to the equation: Ix+Iy=Iz where Ix,Iy,Iz is the moments of inertia about the x-axis, y-axis and z-axis. A flat circular coil has n windings and radius r. The mass of the coil is m. The coil is located in the x-y plan...

I have never dealt with moment of inertia before, this is a physics lab i need to do some pre planning for which involves topics we have never covered and are expected to learn. I've been busy working two jobs and am struggling to get time to pick up this before my lab tomorrow so some help...

Homework Statement for the mass moment of inertia, why did they use Ix/Iy and not Iz? Homework Equations Ix=Iy= 1/12 m (3(r^2) + (h^2)) Iz= 1/2 m (r^2) The Attempt at a Solution

Homework Statement An energy storage system based on a flywheel (a rotating disk) can store a maximum of 4.4 MJ when the flywheel is rotating at 21,300 revolutions per minute. What is the moment of inertia of the flywheel? Homework Equations K= Ktranslational + Krotational Krot=...

Homework Statement Energy is released by the Crab Nebula at a rate of about 5×10^31W, about 105 times the rate at which the sun radiates energy. The Crab Nebula obtains its energy from the rotational kinetic energy of a rapidly spinning neutron star at its center. This object rotates once...

Homework Statement A 2.8-m-diameter merry-go-round with rotational inertia 140kg⋅m2 is spinning freely at 0.40rev/s . Four 25-kg children sit suddenly on the edge of the merry-go-round. a) Find the new angular speed. b) Determine the total energy lost to friction between the children...

How do I find the moment of inertia around the CoM of an object when the axis of rotation is not through the CoM? When Are summation formula used in equations and what exactly constitutes a point mass? regarding moments of inertia?

Hi Guys, It has been a while since my last post but it's great to be back. I am having some trouble with part b) of this question. Don't fully understand the concept and what I'm meant to do. Any guidance or assistance would be greatly appreciated. Thanks in advance you legends!

Hi, Homework Statement I have found the tensor of inertia of a rectangle of sides a and b and mass m, around its center, to be I11=ma2/12, I22=mb2/12, I33=(ma2 + mb2)/12. All other elements of that tensor are equal to zero. I would now like to use this result to determine the tensor of inertia...

Calculate the kinetic energies of two uniform solid cylinders, each rotating about its central axis. They have the same mass, 1.25 kg, and rotate with the same angular velocity, 235 rad/s, but the first has a radius of 0.18 m and the second a radius of 0.73 m. I got 12112188.868 for ω, and...

Homework Statement Which of the following is an inertial frame of reference when the measuring sensitivity in not very high? 1. A frame of reference fixed to the Sun and its axes are pointing toward 3 other stars. 2.A frame of reference fixed to a laboratory table. Homework Equations...

Hello, My question is: how much energy is needed for changing inertia of flywheel? example: on rotary shaft we have linear actuator which is moving some object (mass). by that movement, radius of flywheel is changing. ...if there is energy input to flywheel, mass is moving away form...

Hello, and thank you in advanced for this. I am having trouble with setting up most if not all of my integrals when I am trying to find the elements of an inertia tensor. What would I do if i need to find say the tensor for a disk, but i don't know what to take for my three limits to be. i get...

Homework Statement I've been trying to find out what is the period os this kind of pendulum decribed here: http://www.eng.uah.edu/~wallace/mae364/doc/Labs/mominert.pdf The thing is, I've came to the same result shown in equation (11) but my reasoning it's different. I would even say that...

Homework Statement (a) Calculate the moment of inertia I of the disc when it rotates about the pivot as shown in the figure. (b) If the disc is released from rest, determine the angular speed, ω, of the disc at its lowest point. Homework Equations a) Id = Icm + md^2 Icm = 1/2*M*R^2...

I need to find the moment of inertia of a sphere of radius ##r## and mass ##m## about an axis through it's centre. I've already done it and got the correct answer of ##\frac{2}{3}mr^2## however I have tried doing it using a different method to see if I get the same answer, but I don't, and I...

hi everyone, help me, To calculate the mass moment of inertia at output shaft with respect to input shaft in the two stage planetary gearbox. Torque at input = 15 Nm input speed = 1440rpm stage I zs=14 zp=23 zR=61 fixed stage II zs=21 zp=40 zR=102 fixed

I read that for a rotating body the kinetic energy ##E_k = \sum \frac{1}{2}mv^2 = \frac{1}{2}{\omega}^2∑mr^2 = \frac{1}{2}I{\omega}^2## where ##I## is the moment of inertia. If we did the same thing for momentum then ##P = ∑mv = \omega\sum mr## So why is angular momentum ##I\omega=\omega\sum...

In classical mechanics you want to calculate the moment of inertia for hollow & solid: lines, triangles, squares/rectangles, polygons, planes, pyramids, cubes/parallelepiped's, circles, ellipses, parabola's, hyperbola's, sphere's, ellipsoid's, paraboloid's, hyperboloid's, cones & cylinder's...

Homework Statement Calculate the moment of inertia of a cube which rotates along an axis along its diagonal. Homework Equations Moment of inertia definition: I = \int \rho (\vec{r}) \vec{r} ^2 dV Angular velocity vector; \vec{\omega}=\omega (\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}...

Homework Statement I have tried this thrice now, to no avail. Please help me. Here is the problem: "In the figure, block 1 has mass m1 = 430 g, block 2 has mass m2 = 580 g, and the pulley is on a frictionless horizontal axle and has radius R = 4.9 cm. When released from rest, block 2 falls 74...

Homework Statement Find the moment of inertia of a hollow sphere about a vertical axis through its center in terms of its mass M and radius R. Homework Equations I=\int r^{2} dm The Attempt at a Solution I've been curious about different methods for finding moments of inertia...

Inertia -- Why does it exist? Can someone explain to me in terms of a thought experiement (not equations, please) why it is that inertia exists given that motion is only defined as it relates to another point of reference and given that there is no fixed point of reference but everything is...

Homework Statement My textbook says that I = (1/3)ML^2 for a slender uniform rod, and I = (1/2)MR^2 for a uniform solid cylinder. So let's say that there is cylinder that is a thin disk with M = 5kg, and R = 7m. And let's say that a thin rod also is 5kg and has a length of 7m. Why don't...

Hi, So recently I read about the massive 3 gorges dam changing the mass moment of inertia of the Earth to such an extent that the days will now be 60ns longer. Then I thought, how will this effect the orbit of the Earth about the Sun? Any thoughts?

When all the 4 wheels are braking,it seems logical to write the longitudinal acceleration like this- $$m_{vehicle}.a_x = Sum of F_B $$ Where F_B are the brake forces at the 4 wheels. Now,what would the equation look like when ABS is working? Some of the wheels would be braking while...

Answer check please -- Moment of Inertia Calculations For question 1 I got T=mnut * r pulley * gravity For question 2 I got Isystem = 1/2 M(R23 + R24 + m (R21 + R22) First day of physics lab and I just wanted to double check that these are correct. Thanks.

Homework Statement A thin disk is 100g. It's diameter is 20cm. It's thickness is 2cm. Rotation is about the central axis (ie. perpendicular to the symmetrical plane). Answer in kg*m2 Homework Equations I=(1/2)MR2 M is the mass R is the radius I is the moment of inertia The...

Hi, so i have a fairly good understanding of most of the concepts relating to inertia. but my question is what is the force felt by the observer while accelerating. for example the force gravity can be described as space bending into shapes around the body of mass, the other can be described as...

Two cars move at a speed of 16 meters per second. Each of them has a passenger that is not wearing the seat-belt. Both of these cars decelerate abruptly. Car number one completely stops in 0.25 seconds. Car number two completely stops in two seconds. We know that in both cases, the passengers...

Homework Statement a rod of mass M and length L is supported by a smooth horizontal floor and leans against a smooth vertical wall, the mass density increases linearly with p=kr where r is the distance from the wall and k is a positive constant. a.finf the moment of inertia of the rod with...

I am computing the \hat{I} - moment of inertia tensor - of a cylinder with height 2h and radius R, about its axis of symmetry at the point of its centre of mass. I am working in cartesian coordinaes and am not sure where I am going wrong. (I can see the cylindirical coordiates would be the...

Hi, Consider a 2D laminar only rotating about the z axis, with the axis origin at the bottom left hand corner and adjacent sides coinciding with the z and x axes. so ω = (0,0,ωz) y = 0 I don't understand how the IXZ component is 0 to just leave the IZZ component?

Homework Statement A homogeneous catenary ##z=acosh(x/a)##, ##y=0## and ##x\in \left [ -a,a \right ]## is given. Calculate the center of mass and moment of inertia Homework Equations The Attempt at a Solution I started with ##x=at##, for##t\in \left [ -1,1 \right ]##, therefore...

Ok, so the system consists of two massive spheres, m1 and m2, of radii a and b respectively, connected by a massless rod of length R, as seen in the diagram attached. The question is to calculate the moment of inertia tensor. Sol: Set the origin at the centre of mass . So that we are in...

Homework Statement Homework Equations The Attempt at a Solution With this problem and in general, I am having difficulties knowing what should be the cubic and what shouldn't be from visual inspection, so in this case I can't tell why I_x is 1/12ba^3, as opposed to 1/12ab^3. How can I tell...

Hello, I have the Perimeter Institute Activity Package on Special Relativity and I am working through the problems to teach to my students and I am stuck on the following scenario: The answer for this is given and reads: Now, the point of this question is to get students to think of...