Find the moments of inertia Ix, Iy, I0 for a lamina in the shape of an...

Find the moments of inertia Ix, Iy, I0 for a lamina in the shape of an isosceles right triangle with equal sides of length a if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. (Assume that the coefficient of proportionality is k, and that the lamina lies in the region bounded by x = 0, y = 0, and y = a-x).

Question: in other answers, they state that p(x, y) = k(x^2+y^2) but I'm having a difficult time understanding how they came up with that? A step by step process would be greatly appreciated.

Solutions

Expert Solution

I hope this is clear enough. If you have any other doubts, don't hesitate to ask. That's how we learn.

Thank you!

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

Find the moment of inertia Ix of particle a with respect to the x axis

Find the moment of inertia Ix of particle a with respect to the x-axis (that is, if the x-axis is the axis of rotation), the moment of inertia Iy of particle a with respect to the y axis, and the moment of inertia Iz of particle a with respect to the z-axis (the axis that passes through the origin perpendicular to both the x and y axes). Express your answers in terms of m and r separated by commas.

A lamina with constant density ρ(x, y) = ρ occupies the given region. Find the moments...

A lamina with constant density ρ(x, y) = ρ occupies the given region. Find the moments of inertia Ix and Iy and the radii of gyration and . The part of the disk x2 + y2 ≤ a2 in the first quadrant

Find the mass and center of mass of the lamina with the given density. Lamina bounded...

Find the mass and center of mass of the lamina with the given density. Lamina bounded by y = x2 − 7 and y = 29, (x, y) = square of the distance from the y−axis. Enter exact answers, do not use decimal approximations.

Calculate the moments of inertia (about any axis through the center) for a spherical shell and...

Calculate the moments of inertia (about any axis through the center) for a spherical shell and a solid sphere. What is the ratio between the two moments of inertia. Both spherical shell and solid sphere have mass M, radius R, and uniform mass densities (σ and ρ respectively).

Using the kinematic data provided, calculate the masses, CoM coordinates, and moments of inertia (about the...

Using the kinematic data provided, calculate the masses, CoM coordinates, and moments of inertia (about the proximal end of the segment) for the foot and shank segments (mass: 48.1 kg) (knee: (0.268,0.499)) (ankle: (.240, 0.113)) (Met: (.359, 0.043))

We will find the Moment of Inertia Moment and Polar Moment of Inertia of a U...

We will find the Moment of Inertia Moment and Polar Moment of Inertia of a U profile that will determine its dimensions by ourselves.

Find the mass and center of mass of the lamina that occupies the region D and...

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is bounded by y = 1 − x2 and y = 0; ρ(x, y) = 5ky m= (x bar ,y bar)=

Use source transformation on the circuit shown in Fig 4.98 to find Ix.

Use source transformation on the circuit shown in Fig 4.98 to find \( I_x \) .

For the shape shown below, calculate the moment of inertia about the x axis. (Figure 8)The...

For the shape shown below, calculate the moment of inertia about the x axis. (Figure 8)The dimensions are d1=345 mm, d2=160 mm, d3=120 mm, and r=80 mm. For the shape from Part C (shown again here for reference), calculate the moment of inertia about the y axis.(Figure 8)The dimensions

find the center of mass of a lamina with constant density which is bound. y= 2-√...

find the center of mass of a lamina with constant density which is bound. y= 2-√ (4x-x²) , 2+√ (4x-x²) and the y-axis

Subjects