Lectures by James L. Pazun 6 Circular Motion and Gravitation Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Goals for Chapter 6 To understand the dynamics of circular motion. To study the unique application of circular motion as it applies to Newtons Law of Gravitation. To examine the idea of weight and relate it to mass and Newtons Law of Gravitation. To study the motion of objects in orbit as a special application of Newtons Law of Gravitation. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley In section 3.4 We studied the kinematics of circular motion. Centripetal Acceleration Changing velocity vector Uniform Circular Motion We acquire new terminology. Radian Period Frequency Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Velocity changing from the influence of a c - Figure 6.1 A review of the relationship between v and a c. The velocity changes direction, not magnitude. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Details of uniform circular motion - Example 6.2 Notice how v becomes linear when F c vanishes. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Model airplane on a string - Example 6.1 See the worked example on page 164. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley A tetherball problem Example 6.2 and Figure 6.5 Refer to the worked example on page 165. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Rounding a flat curve Example 6.3 and Figure 6.6 The centripetal force coming only from tire friction. Refer to the worked example on page 166. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Rounding a banked curve Example 6.4 and Figure 6.7 The centripetal force comes from friction and a component of force from the cars mass Refer to the worked problem, Example 6.4. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Dynamics of a Ferris Wheel Example 6.5 and Figure 6.8 Refer to the worked example on page 168. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Walking approximated with U.C.M. Figure 6.10 Each stride is taken as one in a series of arcs Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Newtons Law of Gravitation Figure 6.12 Always attractive. Directly proportional to the masses involved. Inversely proportional to the square of the separation between the masses. Masses must be large to bring F g to a size even close to humanly perceptible forces. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley A diagram of gravitational force Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley The gravitational force calculated Example 6.6 Use Newtons Law of Universal Gravitation with the specific masses and separation. Refer to the worked example on page 172. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley This may be done in a lab. Figure 6.13 The slight attraction of the masses causes a nearly imperceptible rotation of the string supporting the masses connected to the mirror. Use of the laser allows a point many meters away to move through measurable distances as the angle allows the initial and final positions to diverge. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Even within the earth itself, gravity varies. Figure 6.16 Distances from the center of rotation and different densities allow for interesting increase in F g. See the worked example on pages Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Gravitational force falls off quickly. Figure 6.15 If either m 1 or m 2 are small, the force decreases quickly enough for humans to notice. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Gravitation applies elsewhere. Figure 6.17 See the worked example on pages Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley What happens when velocity rises? Figure 6.19 Eventually, F g balances and you have orbit. When v is large enough, you achieve escape velocity. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley Calculations of satellite motion Figure 6.21 Work on an example of a relay designed to stay in orbit permanently. See the solved example on page 177. Copyright 2012 Pearson Education, Inc. publishing as Addison-Wesley If an object is massive, even photons cannot escape. A black hole is a collapsed sun of immense density such that a tiny radius contains all the former mass of a star The radius to prevent light from escaping is termed the Schwarzschild Radius The edge of this radius has even entered pop culture in films. This radius for light is called the event horizon