1. Ch. 6 FORCE AND MOTION  II 6.1 Newton’s Law in Non-inertial Reference Frames 6.1.1Inertial force in linear acceleration reference frame From the view of the ground: where the spring acting on the ball provides the force for the forward acceleration motion.

2. However, in the view of an observer rest at the acceleration vehicle, the ball exerted by a spring force but keep in stationary. To explain this phenomenon, an inertial force is introduced into its force diagram: We have Therefore,

3. 6.1.2Inertial force of centrifugation In natural coordinates, a ball rotating with the plate sustaining a centripetal force:

4. However, in the view of an observer rest at the rotating plate, the ball exerted by a tensile force but kept in stationary. To explain this phenomenon, an inertial force of centrifugation is introduced into its force diagram: Therefore,

5. 6.1.3Coriolic’s force In the view of ground, the mass m, which is moving along the radius direction, sustains a force by the string perpendicular to the radius direction. This force produce a transverse acceleration.

7. However, in the view of an observer rest at the rotating plate, the ball exerted by a force in transverse direction but without a motion in this direction. To explain this phenomenon, a Coriolic’s force is introduced: This imaginary force is called Coriolic’s force. Its magnitude is Considering together with the direction, it can be expressed in terms of cross product as

8. 6.2 Galilean Relativity 6.2.1Galilean transformations

9. 6.2.2Galilean relativity All the inertial reference frames are equivalent. Acceleration is invariant to the choice of inertial system: Generalizing, we assert that there exists a system of mechanics, based on Newton’s laws of motion and called Newtonian mechanics, that describes particle motion in our everyday work to high accuracy. A principle of relativity goes with it: Galilean relativity. For Newtonian mechanics, there is no preferred inertial reference system.

10. Problems: 1. 1.6-41 (on page 115) 2. 2.6-42 3. 3.A ramp with a mass of M in on a frictionless table. A block has a mass of m slides down from the ramp (see figure 1). There is no friction between the block and the ramp. What are their accelerations? What is the acceleration of m relative to M? FIGURE 1

11. 4. 4.Assume that the Earth is a sphere and that the force of gravity (mg) points precisely toward the center of the Earth. Taking into account the rotation of the earth about its axis, calculate the angle between the direction of a plumb line and the direction of the Earth’s radius as a function of latitude. What is this deviation at a latitude of 45 . 5. 5.A mass is attached to the lower end of a string of length l; the upper end of the string is held fixed. Suppose that the string initially makes an angle  with the vertical. With what horizontal velocity must we launch the mass so that it continues to travel at constant speed along a horizontal circular path under the influence of the combined forces of the tension of the string and gravity? This device is called a conical pendulum.