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Lecture17

# Lecture17 - For a system of n particles M = tot mass system...

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For a system of n particles: x CM = m i x i M i =1 n M = tot mass system CM in more than 1D r CM = m i r i M i =1 n y CM = m i y i M i =1 n x CM = m i x i M i =1 n For each component r M dm r CM = For a system of solid object:

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Example Determine the center of gravity of uniform thin rod of length L M

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Example Determine the center of mass of a thin semicircle d θ dm θ r d θ dm θ r y=rsin θ x=rsin θ The semicircle is symmetric with respect to the y axis, hence x CM = 0
Example A disk of radius R is removed from a circular metal plate of Radius 2R. Find the center of mass of the plate 2R R The plate is symmetric about the x axis: the part above x Is symmetric with the part below. The CM is along x Note : Even before calculating the position of the CM we know that it has to lie to the right of the y axis, as there is more mass to the right than to the left. CM The problem can be simplified once we realize that we can treat it as a two objects problem: object 1= CM of disk; object 2 = CM of plate. 1) Assume to fill the disk, the CM is at its origin 2) The CM of the full plate is also at its origin 3) Evaluate the CM of the system made out of two objects

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Motion of a rigid body The general motion of a rigid body (i.e. not pure rotation about a fixed axis) can be described as a translation of the center of mass, plus rotation about the center of mass. Kinematics r CM (t) v CM (t) a CM (t) Refers to motion of center of mass θ (t) ω (t) α (t) Refers to rotation about an axis through the center of mass, which travels with the center of mass.

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Lecture17 - For a system of n particles M = tot mass system...

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