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-coordinatesystem. 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 theobjects are m, = 2.50 kg, m, = 2.50 kg, m, = 4.30 kg, and ma = 2.10 kg.m,m26.00 mmm34.00 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 · 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 • m2Need Help?Read ItPage 2 o

Answer:- Given Mass (m1) = 2.50 kg Mass(m2) = 2.50 kg Mass(m3) = 4.30 kg Mass(m4) = 2.10 kg We know that The moment of inertia of a mass m placed r meters from the axis of rotation I = m r2 (a) This is an additive quantity. Therefore, the moment of inertia around x-axis Ix = m1r12 + m2r22 + m3r32 + m4r42 We know that r1 = r2 = r3 = r4 = 3 m Ix = ( 2.50 + 2.50 + 4.30 + 2.10) × (3)2 Ix = (11.4) × 9 Ix = 102.6 kg m2 (b) Rotation around y axis Iy = m1r12 + m2r22 + m3r32 + m4r42 We know that r1 = r2 = r3 = r4 = 2m Iy = ( 2.50 + 2.50 + 4.30 + 2.10) × (2)2 Iy = (11.4) × 4 Iy = 45.6 kg m2 (C) Rotation around Z axis Iz = m1r12 + m2r22 + m3r32 + m4r42 We know that r1 = r2 = r3 = r4 = (22+32)1/2 = (4+9)1/2 = (13)1/2 Iz = ( 2.50 + 2.50 + 4.30 + 2.10) × (131/2 )2Iz = (11.4) × 13 Iz = 148.2 kg m2

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Physics

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, = 2.50 kg, m, = 2.50 kg, m, = 4.30 kg, and m = 2.10 kg. y m m2 6.00 m m +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 - 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 · m2

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, = 2.50 kg, m, = 2.50 kg, m, = 4.30 kg, and m = 2.10 kg. y m m2 6.00 m m +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 - 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 · m2

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)...

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Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

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Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

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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, = 2.50 kg, m, = 2.50 kg, m, = 4.30 kg, and ma = 2.10 kg.
m,
m2
6.00 m
m
m3
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 · 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
Need Help?
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