Centre of Mass Flashcards
What is the centre of mass equation for a line?
Mx̄ = Σmx
M being total mass
x̄ being centre of mass
mx being mass x distance along line
What is the centre of mass for a triangle?
Intersection of the medians
(x + x + x)/3 , (y + y + y)/3
2/3 along median from vertex
What is the centre of mass for a sector?
In formula book
(2r sinα ) / 3α
with 2α being angle of sector and α being angle above and below centre of mass
What is the centre of mass for a wire?
In formula book
(r sinα ) / α
with 2α being angle of sector and α being angle above and below centre of mass
What is the centre of mass for a solid hemisphere?
In formula book
3r/8 from centre upwards
What is the centre of mass for a hollow hemisphere?
In formula book
r/2 from centre upwards
What is the centre of mass for a solid cone/pyramid?
In formula book
h/4 from centre upwards
What is the centre of mass for a hollow cone?
In formula book
h/3 from centre upwards
What is the centre of mass for a lamina?
x̄ = (∫ xf(x) dx ) / ∫ f(x) dx ) ȳ = 1/2 (∫ f(x)² dx ) / ∫ f(x) dx )
What is the centre of mass for a volume of revolution?
ȳ = 0 x̄ = (∫ xy² dx ) / ∫ y² dx )
If a rigid body is suspended where will it hang?
Vertically below the centre of mass
How do you work out the point of toppling?
θ ≤ arctan (x/y)
θ is the inclination of the plane
x/y is the distance from the origin to the centre of mass
What are the conditions for sliding?
mgsinθ > μR
mgsinθ > μmgcosθ
tanθ < μ
