The figure below shows four particles at the corners of a rectangle, connected by rods of negligible mass. The center of the rectangle lies at theorigin of an xy-coordinate system. The width of the rectangle (along the x-axis) is 4.00 m, and the height (along the y-axis) is 6.00 m. Starting at thetop left and going clockwise, the masses of the particles are m, = 3.10 kg, m2 = 2.10 kg, m3 = 3.70 kg, and m = 2.10 kg.m6.00 mm-4.00 m--(a) What is the moment of inertia (in kg m) of the system about the x-axis?kg m2(b) What is the moment of inertia (in kg m?) of the system about the y-axis?kg-m2(c) What is the moment of inertia (in kg m of the system about an axis through O and perpendicular to the page (that is, the z-axis)?|kg m?Need Help?Read It

Name: The figure below shows four particles at the corners of a rectangle,
Uploaded: 2024-03-20T06:57:37.000Z
Channel: Bartleby
Description: The figure below shows four particles at the corners of a rectangle, connected by rods of negligible mass. The center of the rectangle lies at theorigin of an xy-coordinate system. The width of the rectangle (along the x-axis) is 4.00 m, and the hei

(a) From the figure, the distance of the masses from the x axis is 3.0m. then the moment of inertia…

Science

Physics

The figure below shows four particles at the comers of a rectangle, connected by rods of negligible mass. The center of the rectangle lies at the origin of an xy-coordinate system. The width of the rectangle (along the x-axis) is 4.00 m, and the height (along the y-axis) is 6.00 m. Starting at the top left and going clockwise, the masses of the particles are m, = 3.10 kg, m, = 2.10 kg, mg = 3.70 kg, and m, = 2.10 kg. m 6.00 m m, - 4.00 m-- (a) What is the moment of inertia (in kg m?) of the system about the x-axis? ] kg -m? (b) What is the moment of inertia (in kg m?) of the system about the y-axis? | kg m? (c) What is the moment of inertia (in kg m?) of the system about an axis through O and perpendicular to the page (that is, the z-axis)?

The figure below shows four particles at the comers of a rectangle, connected by rods of negligible mass. The center of the rectangle lies at the origin of an xy-coordinate system. The width of the rectangle (along the x-axis) is 4.00 m, and the height (along the y-axis) is 6.00 m. Starting at the top left and going clockwise, the masses of the particles are m, = 3.10 kg, m, = 2.10 kg, mg = 3.70 kg, and m, = 2.10 kg. m 6.00 m m, - 4.00 m-- (a) What is the moment of inertia (in kg m?) of the system about the x-axis? ] kg -m? (b) What is the moment of inertia (in kg m?) of the system about the y-axis? | kg m? (c) What is the moment of inertia (in kg m?) of the system about an axis through O and perpendicular to the page (that is, the z-axis)?

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter11: Dynamics Of Rigid Bodies

Section: Chapter Questions

Problem 11.2P

See similar textbooks

Similar questions

Two particles of masses m1 and m2 , move uniformly in different circles of radii R1 and R2 R2 about origin in the x, y-plane. The x- and y-coordinates of the center of mass and that of particle 1 are given as follows (where length is in meters and tin seconds): x1(t)=4cos(2t) , y1(t)=4sin(2t) and: xCM(t)=4cos(2t) , yCM(t)=3sin(2t) . a. Find the radius of the circle in which particle 1 moves. b. Find the x- and y-coordinates of particle 2 and the radius of the circle this particle moves.
Where is the center of mass of a slice of pizza that was cut into eight equal slices? Assume the origin is at the apex of the slice and measure angles with respect to an edge of the slice. The radius of the pizza is R.
Find the center of mass of a sphere of mass M and radius R and a cylinder of mass in, radius r, and height h arranged as shown below. Express your answers in a coordinate system that has the origin at the center of the cylinder.
In an elastic collision of two particles with masses m1 and m2, the initial velocities are u1 and u2 = u1. If the initial kinetic energies of the two particles are equal, find the conditions on u1/u2 and m1/m2 such that m1 is at rest after the collision. Examine both cases for the sign of .
Check Your Understanding Suppose we included the sun in the system. Approximately where would the center of mass of the Earth-moon-sun system be located? (Feel free to actually calculate it.)
Where is the center of mass of a semicircular wire of radius R that is centered on the origin, begins and ends on the x axis, and lies in the x, y plane?
A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass ml = 48.0 kg travels in the positive x-direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 = 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities, (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2 and v3 and the sines and cosines of the angles, taking to be the unknown angle, (c) Calculate the final x-components of the momenta of m1 and m2. (d) Calculate the final y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos and v3 sin , respectively, and use the identity cos2 + sin2 = 1 to obtain v3. (g) Divide the equation for v3 sin by that for v3 cos to obtain tan , then obtain the angle by taking the inverse tangent of both sides, (h) In general, would three such pieces necessarily have to move in the same plane? Why?
A projectile of mass 2.0 kg is fired in the air at an angle of 40.0 to the horizon at a speed of 50.0 m/s. At the highest point in its flight, the projectile breaks into three parts of mass 1.0 kg, 0.7 kg, and 0.3 kg. The 1.0-kg part falls straight down after breakup with an initial speed of 10.0 m/s, the 0.7-kg part moves in the original forward direction, and the 0.3-kg part goes straight up. Launch a. Find the speeds of the 0.3-kg and 0.7-kg pieces immediately after the break-up. b. How high from the break-up point does the 0.3-kg piece go before coming to rest? c. Where does the 0.7-kg piece land relative to where it was fired from?
The figure below shows four objects at the corners of a rectangle, connected by rods of negligible mass. The center of the rectangle lies at the origin of an xy-coordinate system. The width of the rectangle (along the x-axis) is 4.00 m, and the height (along the y-axis) is 6.00 m. Starting at the top left and going clockwise, the masses of the objects are: m1 = 2.90 kg, m2 = 1.90 kg, m3 = 4.10 kg, m4 = 2.50 kg. a) What is the moment of inertia (in kg · m2) of the system about the x-axis? ____ kg · m2 (b) What is the moment of inertia (in kg · m2) of the system about the y-axis? _____kg · m2 (c) What is the moment of inertia (in kg · m2) of the system about an axis through O and perpendicular to the page (that is, the z-axis)? _____kg · m2
A rod 2 meters long has a linear density of p(x) = 8 - 3x. How far, in meters, is the center of mass of the rod if measured from the left?
A metal plate has a horizontal width of 3 m and a vertical height of 2 m. The density of the plate is uniform, meaning that the mass is evenly distributed. Let’s consider the origin to be the bottom left of the plate. That means the center of mass of the plate is _____x + _________ym.
If the center of mass of three objects in the xy-plane is given by the location (3 cm, 4 cm) and two of theobjects have the following mass and locations: 5 kg at (3,2), 2 kg at (1, 3) and the third object has mass 8 kg,find the location of the third object.