Wind energy is gaining increased attention, generating an increased interest in windmill technology. Because windmill blades (vanes) rotate about a central axis, one of the most important physical properties of a windmill is its moment of inertia. Given is a picture of a typical windmill, where the geometry and center of mass of one of the vanes is illustrated. The mass of each vane is 309 kg. The distance from the center of mass of the vane to axis B is k₁ = 3.35 m. The distance from the center of mass of the vane to the center of the windmill hub is k₂ = 5.19 m. If the moment of inertia of a vane about axis A is 445 kg-m² and about axis B is 10800 kg-m², calculate the moment of inertia Itotal of the entire assembly about the axis that passes through the windmill's hub and is perpendicular to the screen. (Ignore the hub and assume the vanes are flat.) Itotal = kg.m² Center of mass A B

Wind energy is gaining increased attention, generating an increased interest in windmill technology. Because windmill blades (vanes) rotate about a central axis, one of the most important physical properties of a windmill is its moment of inertia. Given is a picture of a typical windmill, where the geometry and center of mass of one of the vanes is illustrated. The mass of each vane is 309 kg. The distance from the center of mass of the vane to axis B is k₁ = 3.35 m. The distance from the center of mass of the vane to the center of the windmill hub is k₂ = 5.19 m. If the moment of inertia of a vane about axis A is 445 kg-m² and about axis B is 10800 kg-m², calculate the moment of inertia Itotal of the entire assembly about the axis that passes through the windmill's hub and is perpendicular to the screen. (Ignore the hub and assume the vanes are flat.) Itotal = kg.m² Center of mass A B

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Ice skaters often end their performances with spin turns, where they spin very fast about their center of mass with their arms folded in and legs together. Upon ending, their arms extend outward, proclaiming their finish. Not quite as noticeably, one leg goes out as well. Suppose that the moment of inertia of a skater with arms out and one leg extended is 3.2 kg ⋅ m2 and for arms and legs in is 0.80 kg ⋅ m2. If she starts out spinning at 5.0 rev/s, what is her angular speed (in rev/s) when her arms and one leg open outward?
Objects with a uniform mass distribution and a symmetric shape have a center of mass at the center of the object. For non-uniform objects, the center of mass needs to be determined experimentally. To measure the center of mass of such an object, a pivot is placed in the middle of a board and the top of the non-uniform object is placed to the right of the pivot. When a uniform 10.0 kg mass has its center placed 60.0 cm to the left of the pivot the system balances perfectly (as shown below). The mass of the non-uniform object is measured with an electronic scale in the lab and found to beM = 39.8 kg . Top of non-uniform object 10.0 kg M 60.0 cm Part A Where is the center of mass of the non-uniform object? (report the location from the top of the object, and in cm) ΑΣΦ ? dCM = ст
You're watching Disney on ice through a streaming service. Ariel and Aurora 1.4 m/s (each with mass equal to 55 kg), glide in the directions shown (parallel to each other). Their velocities are opposite direction, but both equal to 1.4 m/s. Aurora carries one end of a long massless rod. Their paths are separated by 3.0 m. The other skater grabs the end of the pole as she reaches it. They both then rotate around the center of the rod. For the problems below, assume that there is no friction between the princesses and the ice and we're talking about after the two princesses both hold the rod. 1.4 m/s 1. What is the translational (linear) speed of the two-princess system, specifically, at what speed is the center-of-mass (since everything is symmetric, the c.o.m, is at the center) moving? 2. What is the angular speed of the princesses? 3. What is the kinetic energy of the two-princess system? (continued on second page)
John’s mass is 87.7 kg, and Barbara’s is 59.9 kg. He is standing on the x axis at xJ = +10.3 m, while she is standing on the x axis at xB = +2.10 m. They switch positions. How far and in which direction does their center of mass move as a result of the switch?
A system consists of 2 objects separated by a distance of 7.49m. Object #1 has a mass of 8.08kg and is located a distance of 2.13m away from the center of mass (CM) of the system. The mass of Object #2 is kg.
Problem 11: A merry-go-round at an amusement park consists of an outer ring of horses and an inner ring of elephants. The ring of eight horses has a radius of r = 8.1 m. Each of the eight horses has a mass m, = 95 kg. The ring of four elephants has a radius of r. = 6.4 m and each of the four elephants has a mass m. = 190 kg. The platform of the merry-go-round itself has a mass of m, = 1600 kg and a radius of r, = 10.7 m. At it's operating speed, the merry-go-round makes one revolution every t= 11 s.
in the figure, four point mases are placed as shown. assume that all the numbers in the figure are accurate to two significant figures, What are the x and y cirrdunates if the center of mass (or center of gravity) of this arrangement?
The figure shows a three-particle system, with masses m1 = 4.8 kg, m2 = 4,0 kg, and m3 = 6.9 kg. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass? %3D y (m) mg 2 m1 x (m) (a) Number Units (b) Number i Units