If point c is regarded as a reference, A and B points rotate with a constant rotational speed 3 View the motion from the reference of point C So point c is actually the center of mass
If point c is regarded as a reference, A and B points rotate with a constant rotational speed. View the motion from the reference of point C. So point c is actually the center of mass
Fig 7-5 By building a Cartesian coordinate, position of y point c is found at m11+m C C cn (7-1) m1+m2 or written as mx,+.x cm m1+m2 A (7-2) m,y1+m2y B m1+m2
Fig 7-5 m1 m2 1 r x y O 1 2 1 1 2 2 m m m r m r rcm + + = 1 2 1 1 2 2 m m m x m x xcm + + = 1 2 1 1 2 2 m m m y m y ycm + + = cm r 2 r ' cm r C C’ By building a Cartesian coordinate, position of point c is found at : (7-2) (7-1) or written as: m1 m2 A B C
From Eq(7-1), the velocity and acceleration of the cm are: m, VIt m2 1 cn 21+m (7-4) +m a (7-6) m,+m Can we also find cm is zero from Eg(7-6? 11a1+m2a E+ F 0
From Eq. (7-1), the velocity and acceleration of the CM are: (7-4) (7-6) 1 2 1 1 2 2 m m m v m v dt d r v cm cm + + = = → → → → 1 2 1 1 2 2 m m m a m a dt d v a cm cm + + = = → → → → Can we also find is zero from Eq. (7 cm -6)? a → → → → + = F r + F r m a m a 1 1 2 2 1 2 = 0 → c a → → F2r = − F1r
How about the motion if the system has net external forces? Suppose there is an external force on each particle in above expt, then n,,+m a 2=∑F+∑ f=F+ftf+e 2 2r F+F2=0, and if write∑Fa+∑F2a=∑F ∑Fn n1a+mmoa ntn Newton's second law for ∑ Fen=(m,+m2)acm systems of particles This looks very like a particle of mass m, +m, located the center of mass
How about the motion if the system has net external forces? Suppose there is an external force on each particle in above expt., then This looks very like a particle of mass located at the center of mass. → → → → → → → → m1 a1 + m2 a2 = F1 +F2 = F1ext + F1r + F2ext + F2r 0 1 + 2 = → → F r F r → → → F1ext + F2ext = Fext , and if write → → ext = + cm F (m m )a 1 2 m a + m a =Fext 1 1 2 2 + + = 1 2 1 1 2 2 m m m a m a acm m1 m2 + Newton’s second law for systems of particles