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

What are the mean energy transferred - photon interactions, Photon Interact...

Photon Interactions a. Consider a Si detector of 1 mm thickness. 10 6 photons each with energy of 100 keV are incident on the detector. Find the number of coherent, Compton, an

Resistivity, What components/materials are chosen because of their especial...

What components/materials are chosen because of their especially high resistivity and explain why high resistivity

Ray optics, how do i start studying for this topic where should i start

how do i start studying for this topic where should i start

Exhaust gas temperature, Exhaust gas temperature Monitoring of the temp...

Exhaust gas temperature Monitoring of the temperatures within the engine core is performed by the exhaust gas temperature system. The operating limits of the engine, and monit

Calculate the work done, Problem The work done by a force as it acts o...

Problem The work done by a force as it acts on an object equals the force times the displacement times the cosine of the angle between the force and displacement vectors. a

Examples, Example of like and unlike parallel forces

Example of like and unlike parallel forces

Define the term mach-zchnder interferrometer, Define the term Mach-Zchnder ...

Define the term Mach-Zchnder Interferrometer. Mach-Zchnder Interferrometer The Mach-Zehnder interferometer is a device utilized to find out the phase shift caused through a

Electrical charges, An electron is constrained to the central perpendicular...

An electron is constrained to the central perpendicular axis of a ring of charge of radius 2.2 m and charge 0.015 mC. See Section 22-6. Suppose the electron is released from rest a

Get interference pattern in youngs double slit experiment, What are the con...

What are the conditions to get interference pattern having good contrast in young's double slit experiment

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