Advanced calculus; . 74 DIFFERENTIAL CALCULUS the normals to the arcs AA and. BB at A and £, and the point 0 will approachthe intersection of those normals. The theorem may then be stated that: At any instant of time the motion of arigid body in a plane may be considered as a rotation through an infinitesimal angleabout the intersection of the normals to the paths of any two of its points at that in-stant ; the amount of the rotation will be the distance ds that any point moves dividedby the distance of that point from the instantaneous center of rotation; the angularvelocity about the instant
Advanced calculus; . 74 DIFFERENTIAL CALCULUS the normals to the arcs AA and. BB at A and £, and the point 0 will approachthe intersection of those normals. The theorem may then be stated that: At any instant of time the motion of arigid body in a plane may be considered as a rotation through an infinitesimal angleabout the intersection of the normals to the paths of any two of its points at that in-stant ; the amount of the rotation will be the distance ds that any point moves dividedby the distance of that point from the instantaneous center of rotation; the angularvelocity about the instantaneous center will be this amount of rotation divided by theinterval of time dt, that is, it will be v/r, where v is the velocity of any point of the bodyand r is its distance from the instantaneous center of rotation. It is therefore seenthat not only is the desired theorem proved, but numerous other details are has been stated, the point about which the body is rotating at a given instantis called the ins
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