Rotational inertia Definition and 182 Threads

Homework Statement [/B] A wheel with rotational inertia I = 1/2MR^2 about its horizontal central axle is set spinning with initial angular speed W0. It is then lowered, and at the instant its edge touches the ground the speed of the axle (and CM) is zero. Initially the wheel slips when it...

Homework Statement A uniform disk of radius R=1m rotates counterclockwise with angular velocity ω=2rads/s about a fixed perpendicular axle passing through its center. The rotational inertia of the disk relative to this axis is I=9kg⋅m2. A small ball of mass m=1 is launched with speed v=4m/s in...

Homework Statement I'm given the following four structures with their rotational axes marked, I have to rank them from largest to smallest rotational inertias, I have trouble with that apparently. Homework Equations No equations are really necessary, just my book says the more mass there is...

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...

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...

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...

I think I on the rigth track, would you revise it please 1. A motor is connected to a solid cylindrical drum with a radius of 0.6m and a mass of 52kg. A massless rope is attached to the drum and tied at the other end to a 38kg weight so the rope will wind onto the drum as it turns. The weigth...

Homework Statement A constant horizontal force of magnitude 10 N is applied to a wheel of mass 10 kg and radius 0.30 m as shown in the figure. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.60 m/s2. (a) What are the...

Hi, I would like to calculate the function of a rotating disc that has 2 spring slowing it down. (look at my pictures to understand) Let say I turn my disc 90 degrees clockwise and release it, it is going to oscillate a certain moment than stop. I want to plot that function and to have a...

Hey all, Perhaps this is a bit stupid... I'm familiar with the normal procedure of calculating rotational inertia (using integration, parallel axis theorem, etc.). However, I had a confusing thought: if the center of mass of a body is the point at which you can treat as all of the mass being...

Which would have more rotational inertia? A sphere or cube? Suppose they have the same mass, the side of the cube has the same length as the diameter of the sphere, the cube's rotation axis is perpendicular to two of its faces. Which one would have more rotational inertia about an axis through...

Homework Statement in Attachment Homework Equations I = .5*mr^2 The Attempt at a Solution I have no idea what is going on. This is a pre section quiz and I guessed on one and got it right. I don't know what is meant by the equations not giving I. I googled and noticed I has...

Homework Statement In order to link these into a logical sequence, how do they fit together Homework Equations I = rotational inertia a = angular acceleration (I know a different symbol is usually used) τ= force x moment arm distance The Attempt at a Solution so...to...

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 If we shift the rotation axis from the center of mass of an object, with no change in the orientation of the axis, what happens to the rotational inertia of the object around the axis? Homework Equations Calculating the Rotational Inertia The Attempt at a Solution Does it...

I was taught there was two types of inertia. The translational inertia and the rotational inertia. If in the Earth for example, that has a translational motion around the Sun, and a rotational motion around itself, all forces disappeared, it would follow an uniform rectilinear motion tangent to...

Two masses, 300 g and 400 g, are connected by a cord that passes over a pulley with a radius of 6.64 cm (an Atwood's machine). When released from rest, the 400-g mass falls 60 cm and the 300-g mass rises 60 cm in 4.00 seconds. Find the rotational inertia of the pulley. Four 100-g ice cubes at...

The puzzle is: "The figure below represents a small, flat puck with mass m = 2.24 kg sliding on a frictionless, horizontal surface. It is held in a circular orbit about a fixed axis by a rod with negligible mass and length R = 1.03 m, pivoted at one end. Initially, the puck has a speed of v =...

Hello, I was curious to know if there was some intuitive out-look on why rotational inertia depends on the distance of the mass from the axis of rotation; and why is this distance have to be squared?

Homework Statement Three 2.30kg masses are located at the vertices of an equilateral triangle 55.0cm on a side, connected by rods of negligible mass. Find the rotational inertia, I_2, of this object about an axis that passes through one vertex and the midpoint of the opposite side Homework...

Homework Statement Derive the equation for the linear acceleration of a falling mass m suspended by a string from the rim of a uniform disk of mass M and radius R that is free to rotate without friction about its principal axis. Homework Equations a=rα linear acceleration = radius*angular...

Hey all, I've been thinking about this all night because it been bothering me I need a proper answer for it... Now I have a disc that has mass on each corner(N,W,S,E) it has a total mass of 1 Killo now with the small object spread on its edges. I want to increase the speed of that disc with...

I want to ask why a rod's rotational inertia with rotational axis at its end is not 1/2 mR2 but 1/3 mR2?

Homework Statement A mass M slides down a smooth surface from height h and collides inelastically with the lower end of a rod that is free to rotate about a fixed axis at P as shown below. The mass of the rod is also M, the length is L, and the moment of inertia about P is ML2/3. The angular...

Rotational Inertia "Four point masses problem--diagonal" Homework Statement Four point masses of 3.0 kg each are arranged in a square on mass-less rod. The length of a side of the square is .50 m. What is the rotational Inertia for rotation about an axis passing through masses A and C...

Homework Statement A bowling ball made for a child has half the radius of an adult bowling ball. They are made of the same material (and therefore have the same mass per unit volume). By what factor is a) mass and b) rotational inertia if the child's ball reduced compared with the adult ball...

Homework Statement I have a plot whose vertical intercept is 0.00352 [Nm] If the bearings are 2 [mm] from the center of the wheel, then what is the force of friction? Use three significant figures for your answer in Newtons. Homework Equations Torque= (Rotational Inertia)(Angular...

Homework Statement In the figure below, the pendulum consists of a uniform disk with radius r = 10 cm and mass 480 g attached to a uniform rod with length L = 500 mm and mass 260 g. Homework Equations The Attempt at a Solution I'm going to cut to the chase. I'm basically...

Homework Statement I really don't understand what to do next. A wheel is rotating freely with an angular speed of 950rev/min on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and with twice as much rotational inertia of the first is suddenly coupled on...

So every mountain biker or motocross rider knows to never grab the front brake in the air. When you do the front end drops and can potentially ruin your day in a hurry. I figure that due to the loss of rotational inertia gravity accelerates the front wheel more rapidly, but I would like to see...

Homework Statement A disk of radius r meters has a string wrapped around its perimeter. A mass of m kilograms is attached to the end of the string and is allowed to descend freely from a height of h meters, it takes t seconds for the mass to travel the distance. Find the moment of inertia (I)...

How does friction affect the rotational inertia and angular velocity of a hollow cylinder rolling down an inclined plane? Assuming the cylinder isn't slipping

Homework Statement Two masses are suspended from a pulley system. The pulley itself has a mass of .2kg, a radius of .015m, and a constant torque of .35Nm due to friction between the rotating pulley and its axle. What is the magnitude of acceleration of the suspended masses if m1=.4kg and m2 =...

Block 1 has mass m1 = 460g, block 2 has mass m2 = 500g, and the pulley, which is mounted on a horizontal axle with negligible friction, has radius R = 5.00cm. When released from rest, block 2 falls 75.0 cm in 5.00 s without the cord slipping on the pulley. (a) What is the magnitude of the...

Homework Statement http://apcentral.collegeboard.com/apc/public/repository/ap04_frq_physics_cm_36191.pdf The problem can be found here. I am stuck on problem 2 d. Homework Equations I = m(g-a)R2 / a //found in part c The Attempt at a Solution I don't understand why the...

In Figure, block 1 has mass m1 = 430 g, block 2 has mass m2 = 540 g, and the pulley is on a frictionless horizontal axle and has radius R = 5.3 cm. When released from rest, block 2 falls 80 cm in 5.3 s (without the cord slipping on the pulley). What is the pulley's rotational inertia? Caution...

Homework Statement A small compass needle is situated in a uniform magnetic field. When displaced from its stable equilibrium position through a small angle and then released, it oscillates with a frequency of 5 Hz. A millijoule of work is needed to twist the compass needle round through...

Homework Statement This is a question from the 1999 AP Physics C test. You can view the picture here, on Page 6: http://vhphysics.com/ap/x-test-q/Resource/b)%20Physics%20C%20Materials%20(656)/c)%20AP%20C%20Free-Response%20Problems%20(213)/Physics%20C%201999%20Free%20Response.PDF As...

Homework Statement Given the following Rdisk = 2.50 cm, Raxle = 0.250 cm, Mdisk - 25.0g, Maxle = 0.750g a. Determine the rotational inertia of a yo-yo about it's center. b. Dervie using force and torque the expression for the linear acceleration of a yo-yo c. Calculate the a of the yo-yo...

Homework Statement an irregularly shaped plastic plate with uniform thickness and density (mass per unit volume) is to be rotated around an axle that is perpendicular to the plate face and through point O. The rotational inertia of the plate about that axle is measured with the following...

Hi everyone, I'm having a little trouble trying to answer this problem. Here it is: A force of 22.04 N is applied tangentially to a wheel of radius 0.340 m and gives rise to an angular acceleration of 1.20 rad/s^2. Calculate the rotational inertia of the wheel. Okay so i attempted the...

Homework Statement Four identical particles of mass 0.717 kg each are placed at the vertices of a 3.11 m x 3.11 m square and held there by four massless rods, which form the sides of the square. What is the rotational inertia of this rigid body about an axis that (a) passes through the...

Homework Statement Four identical particles of mass 0.475 kg each are placed at the vertices of a 1.73 m x 1.73 m square and held there by four massless rods, which form the sides of the square. What is the rotational inertia of this rigid body about an axis that (a) passes through the...

Homework Statement alright, so I'm trying to find the rotational inertia of a urethane longboard wheel, and i need to integrate a section of it that looks like a truncated annular cylinder that looks something like this if you cut it in half Homework Equations just to be sure that...

hello, I've gone through countless textbooks and website trying to find the deeper relation between the mass and the radius when calculating the rotational inertia of an object, however know one is giving it up. I know how to calculate the rotational inertia through integration, and i know how...

A bicycle wheel is rolled down a hill that is 8 m high, Determine the linear speed of the wheel at the bottom of the hill if the wheel is moving initially at .5 m/s I= 1/2mr^2 mgh=1/2mv^2 I know it is set up like a KE equation, and I also know I am missing a variable to solve for...

I was in the shop the other day cutting holes out of a 20inx20inx.25in piece of plywood and I noticed that the hole saw was slipping on the board (meaning that it would begin to make an unpleasant sound as the saw hit the board). I had the board clamped down and I realized that a large portion...

Homework Statement A 2.75 m long pole is balanced vertically on its tip. It starts to fall and its lower end does not slip. the mass of the pole is 12.93 kg What is the rotational inertia of the pole about an axis through its lower end and perpendicular to the pole? Homework...

Homework Statement Two skaters, each of mass 50 kg, approach each other along parallel paths separated by 4.0 m. They have opposite velocities of 1.7 m/s each. One skater carries one end of a long pole with negligible mass, and the second skater grabs the other end of it as she passes. The...

1. Homework Statement [/b] I need help with part (a) of this problem. (See attachment) In Fig. 11-45, three particles of mass m = 3.9 kg are fastened to three rods of length d = 0.40 m and negligible mass. The rigid assembly rotates about point O at angular speed ω = 9.1 rad/s. About O...