Chapter 5 Notes Circular Motion and Gravitation
Chapter 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 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
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.
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
Chapter 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
Chapter 5 Centrifugal force vs. centripetal force pg. 116 Read Paragraph out loud Examples 5-3,4,5 & 6 pg
Chapter 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 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 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
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
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
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.