GBK Precalculus
Jordan Johnson
Today’s agenda
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Greetings
Intro & Lesson: Rotary Motion
Classwork / Homework
Announcement: Quiz Friday, 3-1 to 3-7.
Clean-up
A DVD:
Rotary Motion
• As an object rotates, there are multiple
velocities:
▫ Angular velocity: the rotation speed in degrees,
radians, or revolutions per unit of time.
 Most common example: RPM
▫ Linear velocity: the distance a point travels (on
its arc) per unit of time.
Rotary Motion
• Equations:
▫ The angular velocity ω of an object is the rate of
rotation in radians or degrees () over t units of
time:
▫ The linear velocity v of a point is the arc length a
traversed in t units of time:
Conversions:
Linear Velocity  Angular Velocity
• If  is an angle in radians and ω is in radians per
unit of time, then the linear velocity v and arc
length a are given by these equations:
▫ a = r
▫ v = rω
Linear & Angular Velocity
• Audio CDs have a
constant linear
velocity of 1.2 m/sec.
▫ Angular velocity
depends on the read
head’s position.
▫ Angular velocity is
495rpm at innermost,
212rpm at outermost.
Other Applications
• Tire/engine rotation
• Gear or sprocket ratios
▫ Angular velocity of first
gear/sprocket
▫  linear velocity (rate
of chain/tooth motion)
▫  angular velocity of
second gear/sprocket
Classwork / HW:
• For Monday:
▫ Read Section 3-8 and do:
 Reading Analysis questions
 Q1-Q10
 Problems 1-9 odd, 10, and 11.
▫ Bonus:
 Find the angular velocity of the spinning staff, and
the linear velocity of the light at its end.
Clean-up / Reminders
• Pick up all trash / items.
• Push in chairs (at front and side tables).
• See you tomorrow!