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 is the principle of millikans oil drop method, Q. What is the principl...

Q. What is the principle of Millikan's oil drop method? Principle This method is foundation on the study of the motion of uncharged oil drop under free fall due to grav

Scalar and vector, example of problems of vector and scalar with solution

example of problems of vector and scalar with solution

Pressure, 3 scenarios: You have an object such as a jar, and you submerge i...

3 scenarios: You have an object such as a jar, and you submerge it under water to 50m depth. (Every 10m down increases pressure by 1 bar, thus the pressure is 5 bar). Scenario 1:

Vertical circular motion, Vertical Circular Motion A mass is in circul...

Vertical Circular Motion A mass is in circular motion within the vertical plane. We show the weight and force exerted through the tension within the string.

Determine the coefficient of maximum static friction, Dalila decides to det...

Dalila decides to determine the coefficient of maximum static friction for wood against wood by conducting an experiment. First she places a block of wood on a small plank; nex

Define the introduction about schrödinger’s atom, Define the introduction a...

Define the introduction about Schrödinger’s Atom. Introduction to the Schrödinger’s Atom: To describe the spectral line puzzle, Bohr came up along with a radical model of t

Simple harmonic motion, composition of two SHM at right angle to each other...

composition of two SHM at right angle to each other and having time period in the ratio of 1: 2

Evaluate the radius of the planet, Instructors Own Problem: 1) On the su...

Instructors Own Problem: 1) On the surface of some strange planet, Mr. Spock finds his weight to be1200N. He then goes 5000km above the surface, and finds his weight to be on

Doppler Effect, Draw a picture of a moving source and the waves surrounding...

Draw a picture of a moving source and the waves surrounding it according to what you observed in this experiment. How does the spacing of the wave-fronts in front of the source com

Is there any way to improve side- emitting viewing, Is there any way to imp...

Is there any way to improve side- emitting viewing? A side emitting light guide is viewed optimally while the contrast among the optic and background is maximized. When the lig

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