Tham khảo tài liệu 'principles of engineering mechanics (2nd edition) episode 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 76 Kinetics of a rigid body in plane motion RiG 0 z but Pi X ntiPi -k m - ứ2RiG wRjG 0 0 0 1 see equation àmịRiũ hence AfG ft Sm R G2 The term Sm 7 iG2 is known as the moment of inertia of the body about an axis through G parallel to the z-axis and is given the symbol IG. IG is also written MkG2 where M is the mass and kG is called the radius of gyration. Thus Mg IG ã and since w is fixed in direction and IG is a constant for the rigid body . d _ A G y ZGW dr For any rigid body in general plane motion we now have three important equations Fx MxG Fy MỹG and Mg IGá Mkc2 jj Should we choose to take moments about some point o other than the centre of mass then from equation we must add a term equal to the moment of the total mass times the acceleration of the centre of mass to the right-hand side of equation . Referring to Fig. ỳ1 Figure Mo IGã rG MaGe It is sometimes convenient to use vector algebra here and we note that the final term of equation is the component of rGxAfaG in the z-direction thus Mo 7G t rG XMaG k Notice that even when Õ 0 Mo is not necessarily zero. This further emphasises the importance of the centre of mass because by its use the kinetics of translation and of rotation may be treated separately. Rotation about a fixed axis A special but common case of general plane motion is rotation about a fixed axis. If the axis of rotation passes through o then the angular velocity of the line OG will be the same as that of the body namely k. Referring to Fig. and using equation we see that the moment about Oz of the external forces is Mo RiimRiủ ứ mịR2 ủlo where Io mtR2 is defined to be the moment of inertia about Oz. coRi X o Figure Also from equation M o IG i rG Mà rG IG Mrc2 Õ Combining the two expressions for Mo. We have Mo Jg MrG2 à Ioà Moment of inertia of a body about an axis Parallel-axes theorem The moment of inertia about the z-axis is defined to .
