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Center of Mass

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

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

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

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Locating Center of Gravity

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Center of Gravity = Balance Point

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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

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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 + …

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

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

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

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

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

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

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Center of Gravity. Definitions Center of gravity (c.g.) = the point located at the center of the object’s weight distribution Center of mass (c.m.) =

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