Chapter 5 Notes

1. Chapter 5 Notes Circular Motion and Gravitation

2. 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 Chapter 5

3. 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 = ar Chapter 5

4. ar = v2/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 ar = v2/r. • Velocity and acceleration vectors are perpendicular to each other at every point in the path for uniform circular motion. Chapter 5

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 Chapter 5

6. 5-2 Dynamics of Uniform Circular Motion • Newton F=ma • Object moving in a circle must be acted on by a force Fr=mar=mv2/r • Net force must be directed toward the center of the circle. • Centripetal force - force directed towards center of circle Chapter 5

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

8. 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 Chapter 5

9. 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 Chapter 5

10. satellite acceleration = ar = v2/r • force accelerating object is earth’s gravity F= mar • GmmE/r2= mv2/r • m = mass satellite • r = rE + height satellite • Example 5-15 pg. 130 Chapter 5

11. 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 Chapter 5

12. 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 Chapter 5

13. 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. Chapter 5