Trig Do Now

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Trig - Do Now

• Take quiz

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Objectives

• 3.4 Angular Speed
• How can we figure out how fast we are moving on a
  ferris wheel if we know how tall it is and how
  long it takes to make a complete rotation?

NJCCCS 4.2.12.A.3
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Angular and Linear Speed

• Angular Speed the amount of rotation per unit of
  time, where ? is the angle of rotation and t is
  the time.
• Linear Speed distance traveled per unit of time

What are some examples of units for rotational
speed?
Lowercase omega
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How do we convert from angular to linear speed?

• Well, you know that s r?, so plug that in for s
  in the linear speed equation.

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Formulas for Angular and Linear Speed
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Example Using the Formulas

• Suppose that point P is on a circle with radius
  20 cm, and ray OP is rotating with angular speed
  of radian per second.
• a) Find the angle generated by P in 6 sec.
• b) Find the distance traveled by P along the
  circle in 6 sec.
• c) Find the linear speed of P.

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Solution Find the angle.

• The speed of ray OP is radian per
  second.

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Solution Find the angle continued

• The distance traveled by P along the circle is

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Solution Find the angle continued

• linear speed

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Example A belt runs a pulley of radius 6 cm at
80 revolutions per min.

• b) Find the linear speed of the belt in
  centimeters per second.
• The linear speed of the belt will be the same as
  that of a point on the circumference of the
  pulley.

• a) Find the angular speed of the pulley in
  radians per second.
• 80(2?) 160 ? radians per minute.
• 60 sec 1 min

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Trig - Homework

• p. 119-121 1-43 odd (worth 10 points due
  Tues.) 
• Test next Friday on Ch. 3