chapter 5 notes circular motion and gravitation. chapter 5 5-1 kinematics of uniform circular motion...

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Chapter 5 Notes Chapter 5 Notes Circular Motion and Circular Motion and Gravitation Gravitation

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Page 1: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5 NotesChapter 5 Notes

Circular Motion and GravitationCircular Motion and Gravitation

Page 2: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

5-1 Kinematics of Uniform 5-1 Kinematics of Uniform Circular MotionCircular Motion

Uniform circular motion - An object that Uniform circular motion - An object that moves in a circle at a constant speed (v).moves in a circle at a constant speed (v).

The magnitude of the velocity remains The magnitude of the velocity remains constant, but the direction of the velocity is constant, but the direction of the velocity is constantly changing.constantly changing.

Acceleration = change in velocity / change Acceleration = change in velocity / change in timein time

Object revolving in a circle is continuously Object revolving in a circle is continuously acceleratingaccelerating

Page 3: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

Review of centripetal accelerationReview of centripetal acceleration

pg. 113 Fig 5-1 & 5-2pg. 113 Fig 5-1 & 5-2 Velocity points tangent to circleVelocity points tangent to circle Change in velocity - points to center of Change in velocity - points to center of

circlecircle Centripetal acceleration - “center Centripetal acceleration - “center

seeking” accelerationseeking” acceleration Centripetal acceleration = aCentripetal acceleration = arr

Page 4: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

aar r = v= v22/r/r

An object moving in a circle of radius r with a An object moving in a circle of radius r with a constant speed v has an acceleration whose constant speed v has an acceleration whose direction is toward the center of the circle and direction is toward the center of the circle and whose magnitude is awhose magnitude is ar r = v= v22/r./r.

Velocity and acceleration vectors are Velocity and acceleration vectors are perpendicular to each other at every point in the perpendicular to each other at every point in the path for uniform circular motion.path for uniform circular motion.

Page 5: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

Frequency (f) - number of revolutions per Frequency (f) - number of revolutions per secondsecond

Period (T) - time required to complete one Period (T) - time required to complete one revolutionrevolution

T = 1/fT = 1/f For an object revolving in a circle at For an object revolving in a circle at

constant speed v: v=2constant speed v: v=2r/T r/T

Example 5-1 & 5-2Example 5-1 & 5-2

Page 6: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

5-2 Dynamics of Uniform Circular 5-2 Dynamics of Uniform Circular MotionMotion

Newton F=maNewton F=ma Object moving in a circle must be acted on Object moving in a circle must be acted on

by a forceby a force

FFrr=ma=marr=mv=mv22/r/r Net force must be directed toward the Net force must be directed toward the

center of the circle. center of the circle. Centripetal force - force directed towards Centripetal force - force directed towards

center of circlecenter of circle

Page 7: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

Centrifugal force vs. centripetal Centrifugal force vs. centripetal force force

pg. 116 Read Paragraph out loudpg. 116 Read Paragraph out loud

Examples 5-3,4,5 & 6 pg. 117-119Examples 5-3,4,5 & 6 pg. 117-119

Page 8: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

5-8 Satellites and Weightlessness5-8 Satellites and Weightlessness

Satellite - put into circular orbit by Satellite - put into circular orbit by accelerating tangentially using rocketsaccelerating tangentially using rockets

too fast - gravity will not confine ittoo fast - gravity will not confine it too slow - gravity will cause it to fall back too slow - gravity will cause it to fall back

to earthto earth

Page 9: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

What keeps a satellite in space?What keeps a satellite in space?

High speed, if it stopped moving it would High speed, if it stopped moving it would fall to earthfall to earth

Satellite is falling, but high tangential Satellite is falling, but high tangential speed keeps it from falling to earthspeed keeps it from falling to earth

Page 10: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

satellite acceleration = asatellite acceleration = arr = v = v22/r/r force accelerating object is earth’s gravityforce accelerating object is earth’s gravity

F= maF= marr

GmmGmmEE/r/r22= mv= mv22/r/r• m = mass satellite m = mass satellite • r = rr = rEE + height satellite + height satellite

Example 5-15 pg. 130Example 5-15 pg. 130

Page 11: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

WeightlessnessWeightlessness

elevator - rest elevator - rest F= ma W-mg=0 W=mgF= ma W-mg=0 W=mg for acceleration upward = positivefor acceleration upward = positive accelerate upward at a : accelerate upward at a : F= ma W-mg F= ma W-mg

= ma W=ma +mg= ma W=ma +mg downward a is negative, W is less than mgdownward a is negative, W is less than mg

Page 12: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

Weightlessness (cont.)Weightlessness (cont.)

upward a=1/2g W=3/2mg experience 3/2 g’s upward a=1/2g W=3/2mg experience 3/2 g’s accelerationacceleration

downward a=-1/2g W=1/2mg experience 1/2g downward a=-1/2g W=1/2mg experience 1/2g accelerationacceleration

if downward acceleration = free fall = gif downward acceleration = free fall = g W=mg-ma W=mg-mg=0W=mg-ma W=mg-mg=0 therefore, you feel weightless - “apparent therefore, you feel weightless - “apparent

weightlessness”weightlessness” Apparent weightlessness on earth - ski jump, Apparent weightlessness on earth - ski jump,

trampolinetrampoline

Page 13: Chapter 5 Notes Circular Motion and Gravitation. Chapter 5 5-1 Kinematics of Uniform Circular Motion  Uniform circular motion - An object that moves

Chapter 5Chapter 5

Satellites fall toward earth, only force Satellites fall toward earth, only force acting on it is gravityacting on it is gravity

Out in space far from the earth - true Out in space far from the earth - true weightlessness occursweightlessness occurs

gravity pull from other planets is extremely gravity pull from other planets is extremely small due to large distances awaysmall due to large distances away

Prolonged weightlessness - red blood cells Prolonged weightlessness - red blood cells diminish, bones lose calcium and become diminish, bones lose calcium and become brittle, muscles lose their tone.brittle, muscles lose their tone.