Moment of solid sphere about axis, Physics

Assignment Help:

Q. Moment of Solid Sphere About Axis?

The instant of enertia for a homogeneous solid sphere about an axis can be found by integrating spherical shells by integrating disks or by solving the equations for the moment of an element of mass throughout the volume. We will utilize the latter.

The instant of a mass element is I = ∫V l2dm, where dm = ρ dV l is the distance of the element from the axis and ρ is the mass density. Note that the distance to an element from the centre of the sphere is r and l = r sin θ where θ is the angle between the axis and the radius, The volume element dV is

dV = (2π l)(dr)(r dθ) = 2πr2 sinθ dr dθ.

ρ =m/V =m/(4/3(π R3))

And dm = ρdv the moment of inertia is        

I = ∫l2dm = ∫ (r sin θ)2ρdV.

2169_Moment of Solid Sphere About Axis.png

2182_Moment of Solid Sphere About Axis1.png

It is convenient to alter the variable of integration from θ to - cos θ.

Let x = - cos θ Then the limits of the above integral become

1681_Moment of Solid Sphere About Axis2.png

The corresponding integral is

1286_Moment of Solid Sphere About Axis3.png

Finally,

I =2/5(mR2).


Related Discussions:- Moment of solid sphere about axis

Motion on inclined plane, a body is thrown horizontally with a velocity of ...

a body is thrown horizontally with a velocity of u from the top of a tower. the displacement of the stone when the horizontal and vertical velocities are equal is

Science/math, an oven is turned on at a room temperature of 20C and it take...

an oven is turned on at a room temperature of 20C and it takes 10 min to reach a temperature of 190C.a try of cookies is placed in the oven to bake for 10 min.the oven is then turn

Define neutron, Neutron is a fundamental particle which is necessary consti...

Neutron is a fundamental particle which is necessary constituent of all nuclei except that of hydrogen molecule. It was discovered by Chadwick. (1) The charge of neutron: It is

Sound, compostion of two simple harmonic motion

compostion of two simple harmonic motion

What is nuclear radiations, According to Rutherford's experiment when a sa...

According to Rutherford's experiment when a sample of radioactive substance is place in a lead box and permit the emission of radiation by a small hole only. When the radiation ent

Calculate the maximum velocity of rocket, A popular toy on the market some ...

A popular toy on the market some years ago was the water rocket. Water (at 10°C) was loaded into a plastic rocket and pressurized with a hand pump. The rocket was released and woul

Ultrasonic-interferameter , Ultrasonic-interferameter 1.defenition 2.app...

Ultrasonic-interferameter 1.defenition 2.applications 3.uses 4.free lenth 5.Compressibility Ans)An Ultrasonic Interferometer is a easy and direct device to determine the ul

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd