Consider a solid hemisphere of uniform density with radius R. Where is the center of mass? +z O z= 0 O 0 < z < R/2 O z = R/2 O R/2 < z

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Chapter1: Units, Trigonometry. And Vectors
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center of mass of a shell and solid hemisphere

V Examples:
us
ZCM
Consider a solid hemisphere of uniform density with radius R. Where is the center of mass?
+z
O z=0
00<z < R/2
Oz=R/2
O R/2 < z < r
Oz=R
O z=
R.
The center of mass for a solid hemisphere is 3/8 R.
Whereas for a hollow'hemisphere it is 1/2 R.
Centre of mass of hemisphere. Consider a hemisphere of radius R.
(a) Assuming a solid hemisphere with a mass/volume of p, find the centre of mass.
(b) Repeat, assuming the hemisphere is a thin shell with a mass/area of o.
(c) Compare the two values of zCM. Do they make sense?
Transcribed Image Text:V Examples: us ZCM Consider a solid hemisphere of uniform density with radius R. Where is the center of mass? +z O z=0 00<z < R/2 Oz=R/2 O R/2 < z < r Oz=R O z= R. The center of mass for a solid hemisphere is 3/8 R. Whereas for a hollow'hemisphere it is 1/2 R. Centre of mass of hemisphere. Consider a hemisphere of radius R. (a) Assuming a solid hemisphere with a mass/volume of p, find the centre of mass. (b) Repeat, assuming the hemisphere is a thin shell with a mass/area of o. (c) Compare the two values of zCM. Do they make sense?
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