Centre of gravity and moment of inertia, Mechanical Engineering

Centre of Gravity and Moment of Inertia:

-  For a uniform plate of mass M, the overall mass may be divided into individual masses Mi for which centre of gravity is known as (xi, yi), the values of x, y for the centre of gravity of the overall mass is specified by

582_Centre of Gravity and Moment of Inertia.png

and

338_Centre of Gravity and Moment of Inertia1.png

-  Distance of centroid of semicircular area of radius a through the centre is 4 a/3 π

-  Distance of centre of gravity of consistent wire bent into a shape of semicircular arc of radius a from its centre is equal to 2 a /π

-  Theorem I of Pappus and Guldinus

-  The area of the surface produced by revolving a plane curve around a non-intersecting axis in the plane of the curve is equal to the product of (a) length of the curve, and (b) the distance travelled through the centroid G of the curve throughout the revolution.

-  Theorem II of Pappus and Guldinus

-  The volume of solid produced by revolving a plane area A around a non-intersecting axis in its plane is equal to the product of (a) Area A, and (b) the length of the path travelled by the centroid G of the area throughout the revolution w.r.t. axis.

-  Particular parameters of some solids:

1360_Centre of Gravity and Moment of Inertia2.png

-  Area moment of inertia about x axis

1330_Centre of Gravity and Moment of Inertia3.png

 

-  Area moment of inertia about y axis

1482_Centre of Gravity and Moment of Inertia4.png

-  Parallel Axis Theorem : Area moment of inertia about X1 X1 axis at distance y1 from XX = I XX  +  A ( y1 )2

-  Perpendicular Axis Theorem : If z axis is perpendicular to the plane of area A, then =  I z z  = I x x  +  I y y

Posted Date: 1/28/2013 6:34:20 AM | Location : United States







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