Translating observers We consider an inertial observer O and, to start, a translating(possibly accelerating) observer B A/B B Recall that the expression relating the accelerations of a particle A as observed by o, aA, and as observed aB+aA/B Since O is inertial, he or she will be able to verify Newtons second law. Thus, if m is the mass of particle F=m (aB+aA/B) here F is the vector sum of all the forces acting on A. The above equation can be re-writte and, defining the inertial force, Inertial,as Inertial= -maB (5) we can combine the external and inertial forces into the apparent force, Fapparent, to obtain Apparent F+Inertial= maA/ Thus, we see that, if in addition to the external force, we include the inertial force, then observer B, will be able to verify a"modified"Newtons second law. That is, for observer B, the apparent force is equal to the mass times the observed acceleration. This concept is sometimes called D'Alambert's principle, and the inertial force is sometimes referred to as the d'alambert force Although inertial forces manifest themselves as real forces to non-inertial observers, the are sometimes called fictitious. They are called fictitious forces because they do not result from interactions with other bodies, like other forces(e.g. gravity, electromagnetic, contact, etc. ) Fictitious forces"exist"because of the acceleration of the observer Note that when the acceleration of B with respect to O, aB, is zero (i.e. B moves, at most, with a constant velocity with respect to O), then aA =aA/B, which means that B is also inertial, and, hence, Newtons lay verified with respect to BTranslating observers We consider an inertial observer O and, to start, a translating (possibly accelerating) observer B. Recall that the expression relating the accelerations of a particle A as observed by O, aA, and as observed by B, aA/B, is aA = aB + aA/B . (2) 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 = m aA = m (aB + aA/B) , (3) where F is the vector sum of all the forces acting on A. The above equation can be re-written as F − m aB = m aA/B , (4) and, defining the inertial force, Finertial, as Finertial = −m aB , (5) we can combine the external and inertial forces into the apparent force, Fapparent, to obtain Fapparent ≡ F + Finertial = m aA/B . Thus, we see that, if in addition to the external force, we include the inertial force, then observer B, will be able to verify a “modified” Newton’s second law. That is, for observer B, the apparent force is equal to the mass times the observed acceleration. This concept is sometimes called D’Alambert’s principle, and the inertial force is sometimes referred to as the D’Alambert force. Although inertial forces manifest themselves as real forces to non-inertial observers, the are sometimes called fictitious. They are called fictitious forces because they do not result from interactions with other bodies, like other forces (e.g. gravity, electromagnetic, contact, etc.). Fictitious forces “exist” because of the acceleration of the observer. Note that when the acceleration of B with respect to O, aB, is zero (i.e. B moves, at most, with a constant velocity with respect to O), then aA = aA/B, which means that B is also inertial, and, hence, Newton’s law is verified with respect to B. 3