preCalc_5­1_angularANDlinear.notebook
October 31, 2011
Who am I?
Oct 26­12:26 PM
Answers to Evens
p 379
82) 13.96 in
84) 4.712 cm2
86) 0.08 Rad
Oct 26­12:27 PM
1
preCalc_5­1_angularANDlinear.notebook
October 31, 2011
Oct 27­11:27 AM
Oct 27­11:29 AM
2
preCalc_5­1_angularANDlinear.notebook
October 31, 2011
Oct 27­11:37 AM
Angular
v
linear
Velocities
Oct 26­12:27 PM
3
preCalc_5­1_angularANDlinear.notebook
October 31, 2011
Book Print
Jonesian
Vee (Script) ­
Omega
­
(Lower case script)
???
­
Oct 26­12:30 PM
I mean, are these letters or emoticons?
Oct 26­12:36 PM
4
preCalc_5­1_angularANDlinear.notebook
Definition of Linear
Velocity
October 31, 2011
Definition of Angular
Velocity
Relationship Between Both
or
Oct 26­12:37 PM
Angular Velocity (
) ­ has units
of radians per "time"
Linear Velocity (
) ­ has units
of "distance" per "time"
"distance" units must be the same for
linear velocity and radius
Oct 26­12:42 PM
5
preCalc_5­1_angularANDlinear.notebook
October 31, 2011
Ex 1
A child is spinning a rock at the end of a two
foot rope (somebody should buy them a Wii) at
the rate of 180 revolutions per minute (rpm).
Find the linear speed of the rock when it is
released.
Oct 26­12:44 PM
Ex 1
A child is spinning a rock at the end of a two
foot rope (somebody should buy them a Wii) at
the rate of 180 revolutions per minute (rpm).
Find the linear speed of the rock when it is
released.
First: Find the angular velocity
Second: Convert the angular into linear
Oct 26­12:44 PM
6
preCalc_5­1_angularANDlinear.notebook
October 31, 2011
Ex 1
A child is spinning a rock at the end of a two
foot rope (somebody should buy them a Wii) at
the rate of 180 revolutions per minute (rpm).
Find the linear speed of the rock when it is
released.
First: Find the angular velocity
Oct 26­12:44 PM
Ex 1
A child is spinning a rock at the end of a two
foot rope (somebody should buy them a Wii) at
the rate of 180 revolutions per minute (rpm).
Find the linear speed of the rock when it is
released.
Second: Convert the angular into linear
Oct 26­12:44 PM
7
preCalc_5­1_angularANDlinear.notebook
October 31, 2011
Ex 2 (p380 #95)
The mean distance of the Moon from Earth is
2.39 x 105 miles. Assuming that the orbit of the
Moon around Earth is circular and that 1
revolution takes 27.3 days, find the linear speed
of the Moon. Express your answer in miles per
hour.
Oct 26­1:50 PM
Ex 2 (p380 #95)
The mean distance of the Moon from Earth is
2.39 x 105 miles. Assuming that the orbit of the
Moon around Earth is circular and that 1
revolution takes 27.3 days, find the linear speed
of the Moon. Express your answer in miles per
hour.
We Know
r = 239,000 miles
Oct 26­1:50 PM
8
preCalc_5­1_angularANDlinear.notebook
October 31, 2011
Ex 2 (p380 #95)
The mean distance of the Moon from Earth is
2.39 x 105 miles. Assuming that the orbit of the
Moon around Earth is circular and that 1
revolution takes 27.3 days, find the linear speed
of the Moon. Express your answer in miles per
hour.
Oct 26­1:50 PM
Oct 27­12:14 PM
9
preCalc_5­1_angularANDlinear.notebook
October 31, 2011
Ex 3
A bicycle is going down the street with a
linear velocity of 12 mph (5.364 m/s). If the tires
have a radius of 0.28 meters, how many
seconds does it take for the tire to make one
revolution?
Oct 26­2:04 PM
Ex 3
A bicycle is going down the street with a
linear velocity of 12 mph (5.364 m/s). If the tires
have a radius of 0.28 meters, how many
seconds does it take for the tire to make one
revolution?
We Know
v = 5.364 m/s
r = 0.28 m
Oct 26­2:04 PM
10
preCalc_5­1_angularANDlinear.notebook
October 31, 2011
Ex 3
A bicycle is going down the street with a
linear velocity of 12 mph (5.364 m/s). If the tires
have a radius of 0.28 meters, how many
seconds does it take for the tire to make one
revolution?
Oct 26­2:04 PM
Ex 3
A bicycle is going down the street with a
linear velocity of 12 mph (5.364 m/s). If the tires
have a radius of 0.28 meters, how many
seconds does it take for the tire to make one
revolution?
Oct 26­2:04 PM
11
preCalc_5­1_angularANDlinear.notebook
October 31, 2011
Ex 3
A bicycle is going down the street with a
linear velocity of 12 mph (5.364 m/s). If the tires
have a radius of 0.28 meters, how many
seconds does it take for the tire to make one
revolution?
Oct 26­2:04 PM
Assignment
p 380
#s: 88 ­ 90 All
#s: 93 ­ 103 All
(Note: 102 is wicked hard)
Oct 26­2:15 PM
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