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Chapter 5 Notes
Circular Motion and Gravitation
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
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
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
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
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
Centrifugal force vs. centripetal
force

pg. 116 Read Paragraph out loud

Examples 5-3,4,5 & 6 pg. 117-119
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

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 = 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
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.

Chapter 5