O三B In this case, n=0, since the earth rotates with a constant angular velocity, and ab=0 The centripetal acceleration, ac=QX(Q X TA/B), will depend on the point considered and is directe towards the axis of rotation. The modulus is given by ac=RQ2-cos L. For the earth, Q 7.3 x 10-0 rad /s, R=20 x 106 ft, and, if we consider, for instance, a point located at a latitude of L=40, ther ac≈0.08ft/s The Coriolis acceleration, acor= 2nX(UA/B)ry 2, depends on the velocity of A relative to the rotating earth and is zero if the point is not moving relative to the earth. On the other hand, for an aircraft fying i the east-west direction, at a speed of 250 m/s( 718 it/s), acor would be in the radial direction at A (local vertical) and pointing away from the center of the earth(upwards ) The magnitude will b acor≈0.10ft/s2 We see that these values, although not negligible in many situations, are still small when compared with the acceleration due to gravity of g= 32.2 ft/s Inertial forces We know that Newtons second law is only applicable when the motion is referred to inertial observers. This means that, before Newton's second law can be applied, the acceleration measured by a non-inertial observer needs to be transformed to an inertial acceleration. This transformation is achieved using the relative motion expressions derived in the previous lecture. An alternative approach is to extend Newtons second law to general non-inertial observers. This will lead to the concept of inertial forces. We shall see that, in many practical situations, it is convenient to work directly in the accelerated reference frameIn this case, Ω˙ = 0, since the earth rotates with a constant angular velocity, and aB = 0. The centripetal acceleration, ac = Ω × (Ω × rA/B), will depend on the point considered and is directed towards the axis of rotation. The modulus is given by ac = RΩ 2 cosL. For the earth, Ω ≈ 7.3 × 10−5 rad/s, R = 20 × 106 ft, and, if we consider, for instance, a point located at a latitude of L = 40o , then, ac ≈ 0.08ft/s2 . The Coriolis acceleration, acor = 2Ω × (vA/B)x′y′z ′ , depends on the velocity of A relative to the rotating earth and is zero if the point is not moving relative to the earth. On the other hand, for an aircraft flying in the east–west direction, at a speed of 250 m/s (≈ 718 ft/s), acor would be in the radial direction at A (local vertical) and pointing away from the center of the earth (upwards). The magnitude will be acor ≈ 0.10ft/s2 . We see that these values, although not negligible in many situations, are still small when compared with the acceleration due to gravity of g = 32.2 ft/s2 . Inertial forces We know that Newton’s second law is only applicable when the motion is referred to inertial observers. This means that, before Newton’s second law can be applied, the acceleration measured by a non-inertial observer needs to be transformed to an inertial acceleration. This transformation is achieved using the relative motion expressions derived in the previous lecture. An alternative approach is to extend Newton’s second law to general non-inertial observers. This will lead to the concept of inertial forces. We shall see that, in many practical situations, it is convenient to work directly in the accelerated reference frame. 2