Moment of inertia Definition and 1000 Threads

Hello everyone, I have been working on a problem and I am having a hard time figuring out if this is the right answer. Homework Statement A solid sphere of mass 10 kg and radius 10 cm is rotating about its axis. A. Find its moment of inertia B. What is the kinetic energy of the sphere if it...

Homework Statement I am trying to find the moment of inertia of a disc (let the mass be m and radius R) inclined at an angle θ to the vertical axis. (See attachment 1) Homework Equations The Attempt at a Solution I started by taking a small element of area dA. (see attachment 2) The mass of...

What is the differece between the two formulas numbered 3 and 6 in the paint document? And what types of questions would I use eq. 3 and eq. 6?

What is "moment of inertia?" Just curious and I use it a lot but I am not entirely sure what it is. Call me an idiot but I need to know before my physics endeavors proceed.

This just struck me and I was curious.

Homework Statement The total length of the composite body is 4.5 feet. Before the propellant is burned, the projectile weighs 23 lbf. After the propellant burns, the remaining projectile weighs 16 lbf. Before the propellant is burned, the mass center is located 2.6 feet from the projectile...

Hello how can I find the moment of inertia of a circular sector about the X axis , which the sector is symmetrical about , with -θ down and θ above ?! I_{x} = ∫y^{2} dA = ∫y^{2} *y *dx Or =∫∫ y^{2} dy dx I don't know how to put the limits of integration , I turned it to polar...

Homework Statement A uniform beam of mass m = 0.6 kg and length L = 0.3 m can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F1 = 1.5 N, F2 = 1.5 N, F3 = 1.5 N and F4 = 1.5 N. F2 acts a distance d = 0.12 m from the center of...

Homework Statement When calculating moment of inertia of a disk there is something that really bothers me. I've googled this a lot and everywhere i look they 'assume' that the Δa = Δr*2∏r, formula for rectangle, not circle: (area of circle r+Δr - area of circle r) Δa = ∏(r+Δr)^2 - ∏r^2 = ∏r^2 +...

Homework Statement A closed cylindrical tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tube is rotated about a perpendicular bisector, the moment of inertia of water about the axis a)increases b)decreases c)remains constant d)increases if the...

Homework Statement A thin, cylindrical rod = 27.0 cm long with a mass m = 1.20 kg has a ball of diameter d = 10.00 cm and mass M = 2.00 kg attached to one end. The arrangement is originally vertical and stationary, with the ball at the top as shown in the figure below. The combination is...

Homework Statement Two solid spheres -- a large, massive sphere and a small sphere with low mass -- are rolled down a hill. Which one reaches the bottom of the hill first? Homework Equations ICM= (2/5)MR2 The Attempt at a Solution I thought that this would be the smaller sphere...

Homework Statement Suppose you are designing a car for a coasting race -- the cars in this race have no engines, they simply coast down a hill. Do you want large wheels or small wheels? Do you want solid, disk-like wheels, or hoop-like wheels? Should be wheels be heavy or light? (Select all...

Homework Statement Homework Equations I_a = I_G + md^2The Attempt at a Solution I tried using the parallel axis theorem to find the moment of inertia about the axis. In the formula sheet they give the moment of inertia of a hemisphere: I_G = 0.259mr^2, where d, the distance from the center is...

Homework Statement see attachment Homework Equations integration The Attempt at a Solution answers: a. mH2/6 + mt2/12 b. mB2/2 + mt2/12 c. mH2/6 + mB2/2 d. -mBH/4 e. 0, 0 If the plate were thin t can be ignored. Ok so e is because of symmetry so I get that. a-d on the...

Homework Statement A flat object shown here consists of a circle and square made of heavy, uniform wire and welded together at the corners of the square. The mass of the circle is M. The mass of the square is m and its side has a length d. To find the objects moment of inertia about Axis A...

I can't seem to understand moment of inertia. What does it mean and how is it derived ? How does it relate to rotational kinetic energy.

Homework Statement I want to calculate the moment of inertia of a spinning disk via integration. I'm aware of the perpedicular axis theorem, but I want to integrate. Homework Equations I = ∫r^2dm The Attempt at a Solution if I set my coordinate axis op so that the origin of the...

I don't know how to answer these - please please please help! Consider the following objects of mass m rolling down an incline of height h. (a) A hoop has a moment of inertia I = (1/2)mr2. What is the equation for the velocity vhoop of the hoop at the bottom of the incline? (Use the...

Homework Statement See attachment Homework Equations Integrating The Attempt at a Solution The answer is 16pi slug-ft^2. Now I know your suppose to integrate it. Its in 2D, so a double integral at most, maybe a single integral? I'm not very good with integrals and their limits...

To give you a better idea, I have it drawn out here: http://tinypic.com/r/eq6ln5/6 I am calling the thickness of a rod t and the thickness of the shaft t2. I am using the basic equation Ixx = (integrate over area)(y^2)dA on different sections and then adding them all together, following the...

Question for the brilliant minds around here: I'm trying to figure the amount of torque (I*a) needed to rotate a cylinder of a given mass, diameter and length around a pivot point that is off-center. Typically I'm assuming I would find it out by calculating both I for central diameter and end...

Consider a solid disk made of aluminum with a central hole as shown in the figure - can't include...don't believe it's necessary. The external and internal diameters are found to be 13 inches and 0.6 inches. The disk is 0.5 inch thick. The density of aluminum is 2.70 g/cm3. Question: Calculate...

Homework Statement Homework Equations radius of gyration: r = root (I/m) I = moment of inertia m = mass parallel axis theorem given above The Attempt at a Solution Okay, so I think the moment about CM is just m*0.24^2, but after that, I'm less sure. Is the moment about the hip just...

Homework Statement The attachment shows an equilateral triangle of side length "2d" It is a uniform triangle in the 2-D space. Mass of triangle = M I have to find the moment of inertia about one of its side . I am taking the side \overline{AB} as the axis of rotation (hence i would be...

Homework Statement To calculate the moment of inertia of a solid torus through the z axis(the torus is on the xy plane), using the parallel and perpendicular axis theorem. Homework Equations The Attempt at a Solution Well, first I divided the torus into tiny little disks and...

Given some arbitrary shape I can compute the moment of inertia about any axis without a problem by summing the inertia of each of the shapes making up the entire object. I also know the center of mass of the object. Is it possible to directly compute the angles of the axis for the minimum and...

Ok i need some help with some homework that is to derive formula for moment of inertia of a few objects about the axis's that i have mentioned 1. Rectangular slab about axis through center(sides a,b) 2. Annular cylinder about central axis (radii R1 and R2) The only equation i know is...

If you have a tube and a solid cylinder of the same dimensions and density and rolled them down an inclined plane the 'tube' would cover the same distance in less time?

A thin wire of length L and uniformly density ρ is bent into a circular loop with center at O.The moment of inertia of it about a tangential axis lying in the plane of loop is. Ans : Mass M is not given,but ρ is given. So M=ρL3->(1) (L3 means L cube,no idea how to post it in that manner!). For...

We all know that M.I of a Uniform rigid rod about an axis perpendicular to it's length and passing through it's center is MLsquare/12.Where M is mass and L is length of the rod. If it is broken to half such that M becomes M/2 and L becomes L/2,we can't apply ML square /12 formula to it.We have...

Consider a freely rotating body. Let the axis of rotation be the z-axis. For simplicity assume all the mass of the body is concentrated in the x-y-plane, i.e. the plane in which the body rotates. I have read about the moment of inertia tensor on wikipedia, but I don't see how I would combine...

Homework Statement See attached photo Homework Equations The Attempt at a Solution I figured I would use the parallel axis theorem. I'm stuck between two different methods of doing the question, both of which are choices in the answers. My gut instinct says to take the...

Homework Statement The problem is attached in the picture. The Attempt at a Solution I managed to solve it using a different method. I have no idea what the answer is talking about.. My method Found dI of a strip = (1/3)*dm*h2 then i replace h by x, then integrate from -a to...

Hi everyone, good day. this might be a simple question, but I need someone to check my answer. A disk and a hoop, of same mass and same diameter, is first giving a torque (same amount of torque for both) then the torque is removed (the torque is acting on them for the exact same period of...

Homework Statement I did a lab where there was a rotating solid disk with mass= 0.915kg and diameter=0.253m. This was rotating horizontally with an initial angular velocity of 3 different values ω radians/second. After recording the initial angular velocity, I dropped a thin-walled hollow...

I'm trying to understand Moment Of Inertia using integration. But it seems the calculus definition of physics definition are different. (I'm trying to apply my math skill to physics) example of apparent contradiction: here:http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#mi it says the...

Hey i am working on something and i need to know how to calculate moment of inertia of a 3D system of objects. I know these variables: Mass of whole system Center of mass of whole system Center of mass of each object Offset of each object Mass of each object Moment of Inertia of each...

Homework Statement A ball with mass 1.0 kg and radius 0.20m rolls without slipping along level ground with a speed of 10 m/s. The ball then rolls up an incline reaching a maximum vertical height of 8.0 m. What is the moment of inertia of the ball? (Do not assume the ball is a uniform sphere)...

Hello, I am trying to calculate the second moment of inertia for a hollow tube with a reinforcement bar that goes through the tube. The cross section is basically a thin-walled circle (0.1" thickness) with a horizontal bar (about 0.1" thick for now) that spans the diameter of the circle. How...

Homework Statement Beginning with Icm = Integral of r^2 dm from r1 to r2, find the moment of inertia of a solid sphere about any tangential axis. Homework Equations Icm = Integral of r^2 dm The Attempt at a Solution I set up the infinitesimally mass of an infinitesimally...

Homework Statement First, there's a slender rod with length L that has a mass per unit length that varies with distance from the left end, where x=0, according to dm/dx = yx where y has units of kg/m^2. (a) Calculate the total mass of the rod in terms of y and L (Which I've already done and...

This is for prelim study. Just wondering if this solution is correct. Problem A thin homogeneous plate lies in the x-y plane. Its moment of inertia tensor in the x,y,z basis is given by \textbf{I}=σl^{4}\begin{pmatrix} 2 & -2 &0 \\ -1 & 2 & 0 \\ 0 & 0 & 4\end{pmatrix} If the plate...

For calculating I of a uniform solid sphere, why can't we use thin spherical shells? When I try to use spherical shells I get (3/5)MR^2. Every single derivation uses thin cylindrical shells and end up with the correct expression((2/5)MR^2) but they never explain why it is correct to use...

Homework Statement I have three particles of mass m at (-a,-a), (a,-a) and (0,a) Find the moment of inertia I_z around the center of mass of the system for an axis along the z-axis. Homework Equations Center of mass: CM = Ʃmr Moment of inertia: I = Ʃmp^2 m = mass r = position...

Homework Statement A hollow cylinder has mass m, an outside radius R2, and an inside radius R1. Use integration to show that the moment of inertia about its axis is given by I = 1/2*m(R2^2 + R1^2) Homework Equations dm = rho*dV = 2*pi*rho*h*r*dr The Attempt at a Solution This...

Ok, here we go. In a rotating mechanism (helicopter rotor), at a state of equilibrium, the rotor consumes a certain amount of energy from the shaft to maintain a constant angular velocity (since there is a measure of resistance present over the span of the rotor). Lets suppose that the...

In my experiment based on the inertia the angular velocity or speed goes either up or down with the angular momentum remaining the same. I understand that when a person is rotating to change the inertia you would either extend or detract the arms and legs (think dancer). I understand this...

Homework Statement Find the moment of inertia of a circular thin cylindrical surface which ranges from -α/2 to α/2. So looks like - ) The dash being the origin. It basically looks like one fifth of a circular ring. Homework Equations I = mr² The Attempt at a Solution...

Is there a moment of inertia formula for a 2 bladed propeller? If you only have the mass and the length of the propeller, I would think a good estimate would be using a rod rotating about the middle. 1/12ml2