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Derive the formula for the moment of inertia of a uniform, flat, rectangular plate of dimensions&x...
Moment of Inertia
Four small spheres, each of which can be regarded as a point mass of 0.200 kg, are arranged in a square 0.400 m and connected by extremely light rods. Find the moment of inertia of the system about an axisa) through the center of the square O, perpendicular to the plane of the squareb) bisecting two opposite sides of the square (line A-B in the figure)c) passing through O along a diagonal of the squared) Suppose the masses of the...
Physics problem A 3-dimensional object actually has THREE principle moments of inertia - the moments of...
Physics problem
A 3-dimensional object actually has THREE principle moments of inertia - the moments of inertia about the three mutually perpendicular "principle" axes. Take a rectangular book or object that has three different dimensions (length, width and height), so that it has three different moments of inertia, and try to spin it around the three principle axes (the axes that are perpendicular to each face of the object and pass through the center of it). Only one axis produces...
1. Consider a uniform rectangular plate with mass M, side lengths a and 2a, and negligible...
1. Consider a uniform rectangular plate with mass M, side lengths a and 2a, and negligible thickness. In the following, ignore gravitational and frictional forces. a. Identify the principal axes and derive the principal moments of inertia 2a b. The plate is made to rotate with a constant angular velocity around an axis coincident with a diagonal of the rectangle as shown. Express the angular momentum vector in terms of the body coordinate system consisting of the body's principal axes...
Find the Moment of inertia of: a) The rectangular solid formed by 0≤x≤a,0≤y≤b, and 0≤z≤c by...
Find the Moment of inertia of:
a) The rectangular solid formed by 0≤x≤a,0≤y≤b, and 0≤z≤c by
calculating Ix, Iy, Iz. [Hint:
Compute one of the moments directly and then reason about the other
cases via symmetry].
b) The x, y and z axes of a thin plate bounded by the parabola
x=−y2 and the line x=−y with the density function
defined as δ(x,y) = 1/y.
Find the Moment of inertia of: (a) (15 points) The rectangular solid formed by 0...
The cantilevered beam (Figure 1) has a rectangular crosssectional area A, a moment of inertia I,...
The cantilevered beam (Figure 1) has a rectangular crosssectional area A, a moment of inertia I, and a modulus of elasticity E Part A If a load P acts at point B as shown, determine the displacement at B in the direction of P, accounting for bending, axial force, and shear. Express your answer as an expression in terms of the variables P, L, A, E, I, 0, and G and any necessary constants. Submit Provide Feedback Figure 1 of...
The rectangular plate is subjected to the deformation shown by the dashed line. The dimensions are...
The rectangular plate is subjected to the deformation shown by
the dashed line.
The dimensions are X=150 mmX=150 mm, Y=225 mmY=225 mm, and Δy=4
mmΔy=4 mm.
Determine the average shear strain in the plate.
Express your answer to three significant figures. ( rad )
Ay Problem 2.8 The rectangular plate is subjected to the deformation shown by the dashed line X Ay The dimensions are X = 150 mm, Y = 225 mm, and Ay = 4 mm. Part A...
In your physics lab you are given a 11.7-kg uniform rectangular plate with edge lengths 64.7...
In your physics lab you are given a 11.7-kg uniform rectangular plate with edge lengths 64.7 cm by 53.9 cm. Your lab instructor requires you to rotate it about an axis perpendicular to its plane and passing through one of its corners and then prepare a report on the project. For your report you will need the plate's moment of inertia with respect to this axis. Calculate it here first. Number kg m
Problem 23.12 The electric potential of a very large isolated flat metal plate is V. It...
Problem 23.12 The electric potential of a very large isolated flat metal plate is V. It carries uniform distribution of charge of surface density o (C/m), or o/2 on each surface. Part A Determine V at a distance x from the plate. Consider the point to be far from the edges and assume z is much smaller than the plate dimensions Express your answer in terms of the variables V, 0, 2, and appropriate constants. ANSWER: V(2) =
Problem 11.14 Part A A woman of mass m stands at the edge of a solid...
Problem 11.14 Part A A woman of mass m stands at the edge of a solid cylindrical platform of mass M and radius R. At t = 0, the platform is rotating with negligible friction at angular velocity wo about a vertical axis through its center, and the woman begins walking with speed v (relative to the platform) toward the center of the platform. Determine the angular velocity of the system as a function of time. Express your answer in...
QUESTION 2A (11 marks) [Allow 13 minutes] Water flows over a stationary, smooth, flat rectangular plate with dimensions 0.4 x 0.25m as shown in the figure below. The plate has its long axis parallel...
QUESTION 2A (11 marks) [Allow 13 minutes] Water flows over a stationary, smooth, flat rectangular plate with dimensions 0.4 x 0.25m as shown in the figure below. The plate has its long axis parallel to the direction of flow 0.4 m U1 m/s 0.25 m Answer the questions below where the properties of the water are (p 1000 kg/m, v 106 m2/s): a) Determine the nature of the boundary layer over the plate if the approach velocity of the water,...
Physics problem
A 3-dimensional object actually has THREE principle moments of inertia - the moments of inertia about the three mutually perpendicular "principle" axes. Take a rectangular book or object that has three different dimensions (length, width and height), so that it has three different moments of inertia, and try to spin it around the three principle axes (the axes that are perpendicular to each face of the object and pass through the center of it). Only one axis produces...
1. Consider a uniform rectangular plate with mass M, side lengths a and 2a, and negligible thickness. In the following, ignore gravitational and frictional forces. a. Identify the principal axes and derive the principal moments of inertia 2a b. The plate is made to rotate with a constant angular velocity around an axis coincident with a diagonal of the rectangle as shown. Express the angular momentum vector in terms of the body coordinate system consisting of the body's principal axes...
Find the Moment of inertia of:
a) The rectangular solid formed by 0≤x≤a,0≤y≤b, and 0≤z≤c by
calculating Ix, Iy, Iz. [Hint:
Compute one of the moments directly and then reason about the other
cases via symmetry].
b) The x, y and z axes of a thin plate bounded by the parabola
x=−y2 and the line x=−y with the density function
defined as δ(x,y) = 1/y.
Find the Moment of inertia of: (a) (15 points) The rectangular solid formed by 0...
The cantilevered beam (Figure 1) has a rectangular crosssectional area A, a moment of inertia I, and a modulus of elasticity E Part A If a load P acts at point B as shown, determine the displacement at B in the direction of P, accounting for bending, axial force, and shear. Express your answer as an expression in terms of the variables P, L, A, E, I, 0, and G and any necessary constants. Submit Provide Feedback Figure 1 of...
The rectangular plate is subjected to the deformation shown by
the dashed line.
The dimensions are X=150 mmX=150 mm, Y=225 mmY=225 mm, and Δy=4
mmΔy=4 mm.
Determine the average shear strain in the plate.
Express your answer to three significant figures. ( rad )
Ay Problem 2.8 The rectangular plate is subjected to the deformation shown by the dashed line X Ay The dimensions are X = 150 mm, Y = 225 mm, and Ay = 4 mm. Part A...
In your physics lab you are given a 11.7-kg uniform rectangular plate with edge lengths 64.7 cm by 53.9 cm. Your lab instructor requires you to rotate it about an axis perpendicular to its plane and passing through one of its corners and then prepare a report on the project. For your report you will need the plate's moment of inertia with respect to this axis. Calculate it here first. Number kg m
Problem 23.12 The electric potential of a very large isolated flat metal plate is V. It carries uniform distribution of charge of surface density o (C/m), or o/2 on each surface. Part A Determine V at a distance x from the plate. Consider the point to be far from the edges and assume z is much smaller than the plate dimensions Express your answer in terms of the variables V, 0, 2, and appropriate constants. ANSWER: V(2) =
Problem 11.14 Part A A woman of mass m stands at the edge of a solid cylindrical platform of mass M and radius R. At t = 0, the platform is rotating with negligible friction at angular velocity wo about a vertical axis through its center, and the woman begins walking with speed v (relative to the platform) toward the center of the platform. Determine the angular velocity of the system as a function of time. Express your answer in...
QUESTION 2A (11 marks) [Allow 13 minutes] Water flows over a stationary, smooth, flat rectangular plate with dimensions 0.4 x 0.25m as shown in the figure below. The plate has its long axis parallel to the direction of flow 0.4 m U1 m/s 0.25 m Answer the questions below where the properties of the water are (p 1000 kg/m, v 106 m2/s): a) Determine the nature of the boundary layer over the plate if the approach velocity of the water,...
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