a lamina occupies the part of the disk in the first quadrant and the density at each point is given by the function . a. what is the total mass? b. what is the moment about the x-axis, ? c. what is the moment about the y-axis, ? d. where is the center of mass? ( , ) e. what is the moment of inertia about the origin, ?

Question

08-11-2022
Physics

Answered

a lamina occupies the part of the disk in the first quadrant and the density at each point is given by the function . a. what is the total mass? b. what is the moment about the x-axis, ? c. what is the moment about the y-axis, ? d. where is the center of mass? ( , ) e. what is the moment of inertia about the origin, ?

Answer :

Other Questions

The moment of inertia of a uniform rod about an axis through its center is M L 2 / 12. The moment of inertia about an axis at one end is M L 2 / 3. Explain why

Find the kinetic energy of arotating body with moment of inertia 0.003 kgm^2 and angula velocity of 0.6 radius

a possible space habitat of the future is a cylinder in space rotating about its long axis. what is the relative gravitational field along the axis of the habit

what is the energy density at the center of a circular loop of wire carrying a 24.0 a current if the radius of the loop is 27.0 cm ?

A 2.55 kg bucket of sand is attached to a 1.31 m long rope and is swung in a vertical circle. At the bottom of the circle the tension in the rope is 30.2 N. Wha

For a particular nonlinear spring, the relationship between the magnitude of the applied force f and the resultant displacement x from equilibrium is given by t

Air is flowing through a rocket nozzle. Inside the rocket the air has a density of 5. 25 kg/m3 and a speed of 1. 20 m/s. The interior diameter of the rocket is

A student correctly determined the density of two rocks. If the volumes of the two rocks are equal, the rock with the greater density has a.

A massless rope connects a box on a horizontal surface and a hanging stone as shown below. The rope passes over a massless, frictionless pulley. The box is give

A 2 kg stone is tied to a 0. 50-m long string and swung around a circle at a constant angular velocity of 12 rad/s. The net torque on the stone about the center

qwlilly qwlilly · Answer 1 · 2022-11-15T08:32:59-05:00

The center of mass of the lamina would be in the middle of the axis and the mass of the lamina is 25.

For this, we will use the polar coordinates. According to the change of coordinates, where r and theta are the new parameters. Given a point (x,y) in the plane, r is the distance from (x,y) to the origin and theta is the angle formed between the line that joins the origin and the point, and the x-axis.

We need to describe the region D in terms of the new parameters. Replacing the values of x,y in the given inequality, we get that . Since and r>0 we get that r<=5. On the other side, in order to describe the whole region of the first quadrant, we need to sweep the angle theta from 0 to. With that, we can calculate the mass of the lamina as follows here, the extra r appears as the Jacobian coordinates.

Learn more about lamina and refer to numerical at,

https://brainly.com/question/15115409

#SPJ4