Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
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
Q. What is a frame of reference? A system of co-ordinate axes which describe the position of a particle in two or three dimensional space is called a frame of reference.
Le Chatelier's principle (H. Le Chatelier; 1888) If a system is in equilibrium, then any change imposed onto the system tends to shift the equilibrium to decrease the effect of
A 50 newton light fixture is supported by two guy wires as shown. Determine the tension in each wire
What do you mean by a junction diode. Illustrate the formation of depletion layer at the junction. Describe the variation of depletion layer in forward and reverse biased condition
does lights of different wavelengths help us to see different colour
Does upthrust change in different liquids (examples please)
Proton was discovered by: (1)Chadwick (2)Thomson (3)Goldstein (4)Bohr Ans: (3)Goldstein
Determine the average kinetic energy of each type of molecule? A cylinder contains a mixture of helium and argon gas in equilibrium at temperature of 149°C. (a) What is the a
Obtain expression for an optical path difference for formation of circular fringe in Michelson''s interferometer
A hiker tosses a rock into a canyon. He hears it strike water 4.78 s later. How far down is the surface of the water?
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!
whatsapp: +1-415-670-9521
Phone: +1-415-670-9521
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd