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 m,= 3.50 kg, m2= 2.50 kg, m3= 4.30 kg, and m, = 1.90 kg.m,m26.00 mm3+ 4.00 m→(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 • m(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

Part (a) Basic Details The moment of inertia of the system is the product of the mass to that of the…

Answered: The figure below shows four objects at…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter10: Systems Of Particles And Conservation Of Momentum

Section10.3: Center Of Mass Revisited

Problem 10.2CE

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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?
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
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