## Moment of thin spherical shell about axis, Physics

Assignment Help:

Moment of Thin Spherical Shell About Axis

This problem can be set up in spherical coordinates so that conversions from Cartesian coordinates are not required. The mass element for this case is supposed to exist on the surface of a sphere. The element of the surface area of a sphere δS is related to an element of mass by δm = σδS where σ is the mass per unit area ρ = R sin θ is the length of the moment arm for the mass element. Therefore δI = ρ2 δm. The area of the surface element is Rδθ × Rsin θδφ or R2 sin θδθδφ.

Expanding, we have

δI = (Rsin θ)2δm

δI = R2sin2θσ δS

δI = R2sin2θσR2sin θ δθ δφ

δI = R4σ sin3θ δθ δφ

Summing the increments and taking limits, we may write the following integral:  It is prosperous to integrate with respect to φ first. To solve this integral evoke that sin θ dθ = d(- cos θ) Making the substitution mindful that changing the variable of integration requires changing the integration limits as follows We are able to write It perhaps convenient to replace cos θ in 8.3 with a easier variable say x

We now have Noting that the total mass m is σ4πR2 we are able to reduce to

I =2/3mR2

#### Non-horizontally launched projectiles, Non-Horizontally Launched Projectile...

Non-Horizontally Launched Projectiles Assume a cannonball being launched at an angle from cannon atop an extremely high cliff. Suppose as well in which the cannonball does not

#### Matter waves (de-broglie waves), It is described by de-Broglie a moving mat...

It is described by de-Broglie a moving material molecule sometimes acts as a wave and sometimes as a particle. The wave associated with moving particle is known as matter w

#### Explain the procedure of finding miller indices, Explain the procedure of f...

Explain the procedure of finding Miller indices. Procedure of finding Miller indices: a. The intercepts of the needed plane onto the three coordinate axes has to be founded.

#### Foucault pendulum and machs principle, Foucault Pendulum and Mach's Princip...

Foucault Pendulum and Mach's Principle Within theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture) is the name giv

#### Has vc a limit, Has Vc a limit? Answer; precisely, but we do not know i...

Has Vc a limit? Answer; precisely, but we do not know its limit. But we know it is greater than c.

#### Explain frame of reference, FRAME OF REFERENCE:  "A set of reference ax...

FRAME OF REFERENCE:  "A set of reference axis needed to locate the position of an object in space is known as a frame of reference"

#### State kirchoffs second law in electricity., Q. State Kirchoff's second law ...

Q. State Kirchoff's second law in electricity? Kirchoff's second law (voltage law) the algebraic total of the products of resistance as well as current in each part of any

#### .inkjet printer, tell me in detail about inkjet printer???

tell me in detail about inkjet printer???

#### Reflection law, Reflection law For a wavefront intersecting reflecting...

Reflection law For a wavefront intersecting reflecting surface, the angle of incidence is equivalent to the angle of reflection, in the similar plane described by the ray of i

#### Typical signal source and amplifier circuit, 1. Discuss the internal noise ...

1. Discuss the internal noise sources that are present in a typical signal source and amplifier circuit, and describe their effects.  2.  The company currently has a low noise a  