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

Characteristics of simple harmonic motion, a)  Amplitude : It is the main ...

a)  Amplitude : It is the main value of distance of the particle from its equilibrium position. b) Time period (T): Smallest time interval after which the oscillatory motion

What is maser, Q. What is Maser? Give the principle of it. 1) The term...

Q. What is Maser? Give the principle of it. 1) The term MASER for Microwave Amplification through Stimulated Emission of Radiation. 2) The working of maser is similar to th

What is the sum momentum of the combination object, Regard as two cars both...

Regard as two cars both moving eastward along a straight road. Car 1 is in facade of car 2. Car 1 has a mass of 1200 kg as well as a speed of 24 m/s. Car 2 has a mass of 1100 kg as

How is laser in heat treatment use as nuclear fusion, How is laser in heat ...

How is laser in heat treatment use as nuclear fusion? Nuclear fusion A few of the world's most powerful and complicated arrangements of multiple lasers and optical amplifier

Explain the meaning of lasers, Explain the meaning of Lasers? Lasers us...

Explain the meaning of Lasers? Lasers use these discrete energy levels in atoms or molecules to build a large population of atoms at an excited energy level that are ready and

Matlab, contact ball whit wall box

contact ball whit wall box

Expression for current and impedance in series lcr circuit, Get a mathemati...

Get a mathematical expression for current and impedance in series LCR circuit. Reduce an expression for the resonating frequency of an LCR series resonating circuit.

Determine the correction curves, A thermal imager is used to measure the te...

A thermal imager is used to measure the temperature of a target surface (ε = 1) in the test section of a wind tunnel. The thermal imager must view the target though a window. The t

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