Translating/Rotating observers In the more general situation in which the accelerated observer can also rotate, we can also define additional inertial forces so that Newtons second law is satisfied for the accelerating observer, but in this case, the inertial forces must account for the rotational effects k TA/B y Recall that the expression relating the acceleration of a particle A, observed by o, aa, and observed by the translating/rotating observer, B,(aAB)ry2,is aB+(aA/B)xy2/+2n X(UA/B)ry2+nX TA/B+nX(&xTA/B) (6) Since O is inertial, he or she will be able to verify Newtons second law. Thus, if m is the mass of particle F=maa where F is the vector sum of all the forces acting on A. Inserting(6) into the above equation and rearranging he terms, we have F-maB-2mSX(UA/B)ry2/ TA/B-mnx(&X TA/B)=m(aa/B)ry If we define the inertial force, Inertial, as Finertial=-maB-2mnX(UA/B)ry2'-mnXrAB-mnX(Q TA/B), hen. we can write Apparent= F+ Inertial= m(aa/B)ry2 We know that the centripetal acceleration, Sx(nxra/B), points towards the axis of rotation. The inertial force associated with it, Fc=-mn X(nxra/B), is a force that points away from the axis of rotation, and hence, it is sometimes called the centrifugal force. The inertial force for the general translating/rotating observer is comprised of various other terms which will be illustrated in the following lecturesTranslating/Rotating observers In the more general situation in which the accelerated observer can also rotate, we can also define additional inertial forces so that Newton’s second law is satisfied for the accelerating observer, but in this case, the inertial forces must account for the rotational effects. Recall that the expression relating the acceleration of a particle A, observed by O, aA, and observed by the translating/rotating observer, B, (aA/B)x′y′z ′ , is aA = aB + (aA/B)x′y ′z ′ + 2Ω × (vA/B)x′y ′z ′ + Ω˙ × rA/B + Ω × (Ω × rA/B) . (6) Since O is inertial, he or she will be able to verify Newton’s second law. Thus, if m is the mass of particle A, we will have, F = maA , (7) where F is the vector sum of all the forces acting on A. Inserting (6) into the above equation and rearranging the terms, we have F − m aB − 2m Ω × (vA/B)x′y ′z ′ − m Ω˙ × rA/B − m Ω × (Ω × rA/B) = m (aA/B)x′y ′z ′ . (8) If we define the inertial force, Finertial, as Finertial = −m aB − 2m Ω × (vA/B)x′y′z ′ − m Ω˙ × rA/B − m Ω × (Ω × rA/B), (9) then, we can write Fapparent ≡ F + Finertial = m(aA/B)x′y′z ′ . We know that the centripetal acceleration, Ω ×(Ω ×rA/B), points towards the axis of rotation. The inertial force associated with it, Fc = −mΩ ×(Ω×rA/B), is a force that points away from the axis of rotation, and, hence, it is sometimes called the centrifugal force. The inertial force for the general translating/rotating observer is comprised of various other terms which will be illustrated in the following lectures. 5