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
- 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:
- Area moment of inertia about x axis
- Area moment of inertia about y axis
- 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