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390 Molesworth’s pocket-book
Moment of Inektia and Centbe of Gyration.
m — Mass of any particle.
M — Mass of the whole body.
d = Distance of any particle m from axis of
rotation.
2 = Sum.
It = Radius of gyration.
I = Moment of inertia of the whole of the
. particles.
1 =t 2 (m d2) = mcP + w, d2 + mad2 + &fc.
Ij = Moment of inertia about an axis passing
through the centre of gravity.
I2 = Moment of inertia about a parallel axis at
a distance y from the centre of gravity.
y = Distance of centre of gravity from the axis
of rotation.
i2=i1 + m^.
Centre of Gyration from Centre of Motion.
In a bar revolving about one end .. — ’577 length.
2 „ centre .. = • 289
Circular plate revolving about centre = '707 radius.
3 „ its diameter = '5
Sphere about its diameter..........= ’ 6324
Hollow sphere (^insensibly thick) .. = "816
Cylinder revolving about its axis .. = ’707
Cone „ „ .. — • 548 radius of base.
Cone (right angled) revolving about
its apex .......................................= '866 height.
To find the Specific Geavitt of a Substance.
W = Weight of body in air. tv = Weight of body in water.
Specific gravity =
If the substance be lighter than the water, sink it by
means of a heavier substance, and deduct the weight of the
heavier substance. Weight of a cubic tout in lbs. = specific
gravity X 62’425.