Center of Mass

Consider motion of object as if all mass located at C of G.

Center of Gravity – Average position of weight Average position of mass Center of Mass –

C of M does not have to be on the object.

Locating Center of Gravity

Center of Gravity = Balance Point

m1m1 m2m2 m3m3 m4m4 A Στ A = m 1 gx 1 + m 2 gx 2 + m 3 gx 3 + m 4 gx 4 CM (m 1 +m 2 +m 3 +m 4 ) Στ A = (m 1 + m 2 + m 3 + m 4 )g x CM A

m 1 gx 1 + m 2 gx 2 + m 3 gx 3 + m 4 gx 4 (m 1 + m 2 + m 3 + m 4 )g x CM = m 1 x 1 + m 2 x 2 + m 3 x 3 + m 4 x 4 + … x CM = m 1 + m 2 + m 3 + m 4 + …

Calculating CM 2- dimensions Platform: 6.0 m x 6.0 m 100. kg 500. kg 3 corners CM?

Toppling Object is stable if its CG is above its base of support.

More stability if CG is low and base of support is wide.

Calculating Angle of Stability θ h b θ tan θ = h/bθ = tan -1 (h/b)

5.0 cm 8.0 cm To what angle can the block tip before it topples over? 58º

If CG is underneath base of support, object remains stable.