Consider a square plate of side a and mass m located with one corner on the...
Consider a square plate of side a and mass m located with one corner on the origin of the x, y plane. Assuming homogeneous surface density, calculate the inertia tensor (remember that it is still a 3 × 3 object). Then calculate the angular momentum around the origin and the rotational kinetic energy if the square is rotating with angular speed ω about (a) the x-axis and (b) the diagonal through the origin.
Homework Answers
all the calculations have been
done taking a=3, if you require answer in terms of a . Kindly just
substitute limits as 0-a in integration and m((a)^2)/2 in the
calculation of Ix in step b and hence proceed. Hope we were
helpful
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Consider a square plate of side a and mass m located with one
corner on the...
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...
(a) A uniform disk of mass 14 kg, thickness 0.5 m, and radius 0.4 m is located at the origin, oriented with its axis al...
(a) A uniform disk of mass 14 kg, thickness 0.5 m, and radius 0.4 m is located at the origin, oriented with its axis along the y axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the +y axis and look toward the origin at the disk). The disk makes one complete rotation every 0.5 s. What is the rotational angular momentum of the disk? What is the rotational kinetic...
a) A square plate has mass 0.600 kg and sides of length 0.150 m. It is...
a) A square plate has mass 0.600 kg and sides of length 0.150 m. It is free to rotate without friction around an axis through its center and perpendicular to the plane of the plate. How much work must you do on the plate to change its angular speed from 0 to 40.0 rad/s? Express your answer with the appropriate units. b) How much work must you do on the plate to change its angular speed from 40.0 rad/s to...
Calculate the angular momentum for a rotating disk, sphere, and rod. (a) A uniform disk of...
Calculate the angular momentum for a rotating disk, sphere, and rod. (a) A uniform disk of mass 16 kg, thickness 0.5 m, and radius 0.9 m is located at the origin, oriented with its axis along the y axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the +y axis and look toward the origin at the disk). The disk makes one complete rotation every 0.7 s. What is the...
Consider a particle of mass m = 17.0 kg revolving around an axis with angular speed...
Consider a particle of mass m = 17.0 kg revolving around an axis with angular speed ω. The perpendicular distance from the particle to the axis is r = 0.250 mThe kinetic energy of a rotating body is generally written as K=12Iω2, where I is the moment of inertia (also known as rotational inertia) of the body. Find the moment of inertia of the particle described in the problem introduction with respect to the axis about which it is rotating....
Consider a particle of mass m = 22.0 kg revolving around an axis with angular speed...
Consider a particle of mass m = 22.0 kg revolving around an axis with angular speed ω. The perpendicular distance from the particle to the axis is r = 0.250 m . The kinetic energy of a rotating body is generally written as K=1/2Iω^2, where I is the moment of inertia (also known as rotational inertia) of the body. Find the moment of inertia of the particle described in the problem introduction with respect to the axis about which it...
Heres example 10.2 (3) (30 points) In Example 10.2, the moment of inertia tensor for a...
Heres example 10.2
(3) (30 points) In Example 10.2, the moment of inertia tensor for a uniform solid cube of mass Mand side a is calculated for rotation about a corner of the cube. It also worked out the angular momentum of the cube when rotated about the x-axis - see Equation 10.51. (a) Find the total kinetic energy of the cube when rotated about the x-axis. (b) Example 10.4 finds the principal axes of this cube. It shows that...
Question 11 Four equal masses m are located at the corners of a square of side...
Question 11
Four equal masses m are located at the corners of a square of side l connected by essentially massless rods. (Use the following as necessary: m and l.) (a) Find the rotational inertia of this system about an axis that coincides with one side. (b) Find the rotational inertia of this system about an axis that bisects two opposite sides.
Consider a stick of length I, mass m, and uniform mass density. The stick is pivoted...
Consider a stick of length I, mass m, and uniform mass density. The stick is pivoted at its top end and swings around the vertical axis. Assume that conditions have been set up so that the stick always makes an angle with the vertical. a) Figure out what the principal axes are. You do not necessarily need to diagonalize the I 3. matrix. It will be obvious to find them. Calculate the diagonal components of the moment of inertia tensor....
Three masses are connected by rigid massless rods, as shown. The 200-g mass (B) is located...
Three masses are connected by rigid massless rods, as shown. The 200-g mass (B) is located at the origin (0, 0). (a) Find the x- and y-coordinates of the center of mass. (b) Find the moment of inertia of this system of three connected masses when rotated about the r-axis that passes through mass B? (c) If this system is rotated about the r-axis, from rest to an angular speed of 6 rad/s in time t = 3 s, what...
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...
(a) A uniform disk of mass 14 kg, thickness 0.5 m, and radius 0.4 m is located at the origin, oriented with its axis along the y axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the +y axis and look toward the origin at the disk). The disk makes one complete rotation every 0.5 s. What is the rotational angular momentum of the disk? What is the rotational kinetic...
Calculate the angular momentum for a rotating disk, sphere, and rod. (a) A uniform disk of mass 16 kg, thickness 0.5 m, and radius 0.9 m is located at the origin, oriented with its axis along the y axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the +y axis and look toward the origin at the disk). The disk makes one complete rotation every 0.7 s. What is the...
Heres example 10.2
(3) (30 points) In Example 10.2, the moment of inertia tensor for a uniform solid cube of mass Mand side a is calculated for rotation about a corner of the cube. It also worked out the angular momentum of the cube when rotated about the x-axis - see Equation 10.51. (a) Find the total kinetic energy of the cube when rotated about the x-axis. (b) Example 10.4 finds the principal axes of this cube. It shows that...
Question 11
Four equal masses m are located at the corners of a square of side l connected by essentially massless rods. (Use the following as necessary: m and l.) (a) Find the rotational inertia of this system about an axis that coincides with one side. (b) Find the rotational inertia of this system about an axis that bisects two opposite sides.
Consider a stick of length I, mass m, and uniform mass density. The stick is pivoted at its top end and swings around the vertical axis. Assume that conditions have been set up so that the stick always makes an angle with the vertical. a) Figure out what the principal axes are. You do not necessarily need to diagonalize the I 3. matrix. It will be obvious to find them. Calculate the diagonal components of the moment of inertia tensor....
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