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

Process to calculate the velocity of the mass, A 10 kilogram mass rests on ...

A 10 kilogram mass rests on a horizontal frictionless surface.  A horizontal force of 5 Newtons is applied to the mass.  After the force has been applied for 1 second, the

Tunnels through the earth, Q. Tunnels through the Earth Assume a straig...

Q. Tunnels through the Earth Assume a straight tunnel is cut from the surface of the earth to the opposite side through the centre. The object is going down the tunnel and a

A longitudinal wave moves through a medium, As a longitudinal wave moves th...

As a longitudinal wave moves through a medium, the particles of the medium: a) vibrate in a path parallel to the path of the wave b) vibrate in a path perpendicular to the p

Explain continuous x-rays, As an electron passes close to the positive nucl...

As an electron passes close to the positive nucleus of atom, the electron is moved from its path as given in diagram. This results in deceleration of the electron. The loss in powe

Explain insulators, Insulators: Insulators are those substances which d...

Insulators: Insulators are those substances which do not permit to pass electric current by them. e.g. Wood, Plastic, rubber, glass etc

Are there many type of single ends in optics fiber, Are there many type of ...

Are there many type of single ends? Single ends can be no matter which from a simple cut with snips or a cutter to a sophisticated polished encapsulation. The actual method use

Wave motion, What is the difference between vibration and waves?

What is the difference between vibration and waves?

Magnetic domains, Ferromagnetic materials get magnetic properties not only ...

Ferromagnetic materials get magnetic properties not only because their atoms owns a magnetic moment but also because the material consists of small regions called as magnetic domai

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