1. Chapter 5 Notes Circular Motion and Gravitation

2. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves in a circle at a constant speed (v).  The magnitude of the velocity remains constant, but the direction of the velocity is constantly changing.  Acceleration = change in velocity / change in time  Object revolving in a circle is continuously accelerating

3. Chapter 5 Review of centripetal acceleration  pg. 113 Fig 5-1 & 5-2  Velocity points tangent to circle  Change in velocity - points to center of circle  Centripetal acceleration - “center seeking” acceleration  Centripetal acceleration = a r

4. Chapter 5 a r = v 2 /r  An object moving in a circle of radius r with a constant speed v has an acceleration whose direction is toward the center of the circle and whose magnitude is a r = v 2 /r.  Velocity and acceleration vectors are perpendicular to each other at every point in the path for uniform circular motion.

5. Chapter 5  Frequency (f) - number of revolutions per second  Period (T) - time required to complete one revolution  T = 1/f  For an object revolving in a circle at constant speed v: v=2  r/T  Example 5-1 & 5-2

6. Chapter 5 5-2 Dynamics of Uniform Circular Motion  Newton F=ma  Object moving in a circle must be acted on by a force  F r =ma r =mv 2 /r  Net force must be directed toward the center of the circle.  Centripetal force - force directed towards center of circle

7. Chapter 5 Centrifugal force vs. centripetal force  pg. 116 Read Paragraph out loud  Examples 5-3,4,5 & 6 pg. 117-119

8. Chapter 5 5-8 Satellites and Weightlessness  Satellite - put into circular orbit by accelerating tangentially using rockets  too fast - gravity will not confine it  too slow - gravity will cause it to fall back to earth

9. Chapter 5 What keeps a satellite in space?  High speed, if it stopped moving it would fall to earth  Satellite is falling, but high tangential speed keeps it from falling to earth

10. Chapter 5  satellite acceleration = a r = v 2 /r  force accelerating object is earth’s gravity  F= ma r  Gmm E /r 2 = mv 2 /r m = mass satellitem = mass satellite r = r E + height satellite r = r E + height satellite  Example 5-15 pg. 130

11. Chapter 5 Weightlessness  elevator - rest   F= ma W-mg=0 W=mg  for acceleration upward = positive  accelerate upward at a :  F= ma W-mg = ma W=ma +mg  downward a is negative, W is less than mg

12. Chapter 5 Weightlessness (cont.)  upward a=1/2g W=3/2mg experience 3/2 g’s acceleration  downward a=-1/2g W=1/2mg experience 1/2g acceleration  if downward acceleration = free fall = g  W=mg-ma W=mg-mg=0  therefore, you feel weightless - “apparent weightlessness”  Apparent weightlessness on earth - ski jump, trampoline

13. Chapter 5  Satellites fall toward earth, only force acting on it is gravity  Out in space far from the earth - true weightlessness occurs  gravity pull from other planets is extremely small due to large distances away  Prolonged weightlessness - red blood cells diminish, bones lose calcium and become brittle, muscles lose their tone.