3.4 Notes Day 1.notebook
Sect. 3.4 – Angular & Linear Velocity
Objecves
• To discover and relate linear and angular velocity.
• To use linear and angular velocity to solve word problems.
Angular Velocity
The angular velocity of a point moving in a circular path is the angular displacement (in radians), of the point per unit of time.
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3.4 Notes Day 1.notebook
Relang linear/angular velocity
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Linear Velocity
s = arc length
t = time
r = radius
I
II
III
IV
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3.4 Notes Day 1.notebook
If &
then
If
&
then
If
then
&
Variable
Identity
Label
Label
Label
r
radius (distance)
ft
miles
km
s
arc length (distance)
ft miles
km
t
time
hours
minutes
seconds
angle
degrees
radians
revs
linear velocity
mi/hr
km/sec
in/min
angular velocity
rev/min
degrees/sec
radians/minute
v
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3.4 Notes Day 1.notebook
Conversions for linear velocity
Convert 50 mi/hr to in/sec
Find the Linear Velocity for each of the following:
The tip of the minute hand of a clock, if the hand is 5 cm long.
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3.4 Notes Day 1.notebook
Now you try…
The tip of the second hand of a clock if the hand is 16 mm long.
A point on the tread of a tire of radius 12 in, • rotating 25 times per minute.
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A bike wheel with a radius of 12 inches is rotating at a constant rate of 3 revolutions every 4 seconds. What is the linear speed of a point on the rim of this wheel?
A CD player rotates a CD at different speeds depending on where the laser is reading the disc. Assume that information is stored within a 6‐centimeter diameter of the disk.
Find the linear speed of a point on the outer edge of the CD when the CD player is rotating at 200 revolutions per minute.
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3.4 Notes Day 1.notebook
In 17.5 seconds a car covers an arc intercepted by a central angle of 120 degrees on a circular track with a radius of 300 meters. What is the car’s linear speed in meters per second?
The tires of a bicycle have a radius 8 inches and are turning at the rate of 100 revolutions per minute. How fast is the bicycle traveling in miles per hour?
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3.4 Notes Day 1.notebook
HOMEWORK : Velocities worksheet # 1­9
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