Solutions of the Examples Appended to A Treatise on the Motion of a Rigid Body |
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Page 4
... inertia of the body y about a line through its vertex perpendicular to its axis , and therefore · M ( 4a2 + r2 ) , ( Walton's Examples . ) = and ƒ ƒ ( y2 + " ) is the moment of inertia of the cone about x y its axis and = 3 Mr2 , 10 ...
... inertia of the body y about a line through its vertex perpendicular to its axis , and therefore · M ( 4a2 + r2 ) , ( Walton's Examples . ) = and ƒ ƒ ( y2 + " ) is the moment of inertia of the cone about x y its axis and = 3 Mr2 , 10 ...
Page 5
... inertia when that about another parallel axis is known , viz . by passing through a parallel axis at the centre of gravity . The moment of inertia of the axis through O being known by inspection , we get in succession : ( 1 ) that about ...
... inertia when that about another parallel axis is known , viz . by passing through a parallel axis at the centre of gravity . The moment of inertia of the axis through O being known by inspection , we get in succession : ( 1 ) that about ...
Page 6
... inertia of an infinitely thin homogeneous shell between the surface above mentioned and a contiguous one . pa / 1 - e " . da . The result is The integral of this from zero to a is the moment of inertia of the body formed by an ...
... inertia of an infinitely thin homogeneous shell between the surface above mentioned and a contiguous one . pa / 1 - e " . da . The result is The integral of this from zero to a is the moment of inertia of the body formed by an ...
Page 9
... inertia about every axis though the centre of the cube is the same . .. moment of inertia about the diagonal . = moment of inertia about a line through the centre parallel to four of the edges , = } Ma2 . Again , moment about the ...
... inertia about every axis though the centre of the cube is the same . .. moment of inertia about the diagonal . = moment of inertia about a line through the centre parallel to four of the edges , = } Ma2 . Again , moment about the ...
Page 10
... inertia about them are M b2 + c2 5 a2 + c2 a2 + b2 M M 5 5 hence the moment of inertia about a diameter whose direction cosines relatively to these are l , m , n , is = M 5 M 5 { ( b2 + c2 ) l2 + ( a2 + c2 ) m2 + ( a2 + b2 ) n2 } , { a2 ...
... inertia about them are M b2 + c2 5 a2 + c2 a2 + b2 M M 5 5 hence the moment of inertia about a diameter whose direction cosines relatively to these are l , m , n , is = M 5 M 5 { ( b2 + c2 ) l2 + ( a2 + c2 ) m2 + ( a2 + b2 ) n2 } , { a2 ...
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2g h accelerating force Algebra angle angular velocity ball blow c² a² CA² Calculus Cambridge centre of gravity co-ordinate axes cone Conic Sections cos² cube cylinder diameter Differential Differential Calculus direction cosines disc distance dt dt dt dy dx dt dy dt effective force Examples Geometry Hence horizontal action horizontal and vertical HYMERS DR impulse inertia instantaneous axis invariable plane length Let C fig Ma² mass Mk² moment of inertia moves Mr² oscillation P₁ P₂ parallel particle perpendicular plates point of contact position pressure principal axes principle R₁ radius reaction revolves rotation sin² sphere tan² Third Edition Treatise velocities of translation vis viva w₁ w₂ wheel WHEWELL DR аф ᏧᎾ
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