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Angular Velocity Linear Velocity
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Review Angular Displacement ARC LENGTH Known Facts
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Angular Displacement Definition
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ARC LENGTH
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All the Distance and Time Facts
Known Facts All the Distance and Time Facts
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Angular Velocity How Fast
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What Angle Did It Move Through
In What Period of Time
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What Angle Did It Move Through
Angular Displacement In What Period of Time
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What Angle Did It Move Through
Angular Displacement Time In What Period of Time
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What Angle Did It Move Through
Angular Displacement Time In What Period of Time
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Angular Velocity omega omega
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Angular Velocity Formula
is angular velocity measured in radians per unit of time
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t is the length of time measured in units of time
Formula Angular Velocity is angular velocity measured in radians per unit of time t is the length of time measured in units of time
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t is the length of time measured in units of time
Formula Angular Velocity is angular velocity measured in radians per unit of time t is the length of time measured in units of time
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Example Find the angular velocity in radians per second of a wheel turning at 100 rpm
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Example Find the angular velocity in radians per second of a wheel turning at 100 rpm Our Goal rads sec
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This is an Angular Velocity
Example This is an Angular Velocity Find the angular velocity in radians per second of a wheel turning at 100 rpm Angular Displacement 100 rev rads Per Time min sec
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Example Find the angular velocity in radians per second of a wheel turning at 100 rpm 100 rev rads min sec
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Multiply by a Form of One
Example Find the angular velocity in radians per second of a wheel turning at 100 rpm ? 100 rev rads min rev sec Multiply by a Form of One
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All the Distance and Time Facts
Known Facts All the Distance and Time Facts
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Multiply by a Form of One
Example Find the angular velocity in radians per second of a wheel turning at 100 rpm 100 rev rads min 1 rev sec Multiply by a Form of One
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Example Find the angular velocity in radians per second of a wheel turning at 100 rpm 100 rev rads min 1 rev sec
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Multiply by a Form of One
Example Find the angular velocity in radians per second of a wheel turning at 100 rpm 100 rev 1 min rads min 1 rev 60 sec sec Multiply by a Form of One
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Example Find the angular velocity in radians per second of a wheel turning at 100 rpm 100 rev 1 min rads min 1 rev 60 sec sec To the nearest tenth
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You Try
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Just Change Revs per min to Rads per sec
Find the angular velocity in radians per second of a wheel turning at 78.6 rpm Answer to the nearest tenth Just Change Revs per min to Rads per sec
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Answer to the nearest tenth
Find the angular velocity in radians per second of a wheel turning at 78.6 rpm Answer to the nearest tenth Our Goal 78.6 rev rads min sec
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Answer to the nearest tenth
Find the angular velocity in radians per second of a wheel turning at 78.6 rpm Answer to the nearest tenth Our Goal 78.6 rev rads min sec
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Multiply by a Form of One
Find the angular velocity in radians per second of a wheel turning at 78.6 rpm Answer to the nearest tenth Our Goal 78.6 rev rads min 1 rev sec Multiply by a Form of One
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Answer to the nearest tenth
Find the angular velocity in radians per second of a wheel turning at 78.6 rpm Answer to the nearest tenth Our Goal 78.6 rev rads min 1 rev sec
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Multiply by a Form of One
Find the angular velocity in radians per second of a wheel turning at 78.6 rpm Answer to the nearest tenth Our Goal 78.6 rev 1 min rads min 1 rev 60 sec sec Multiply by a Form of One
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Answer to the nearest tenth
Find the angular velocity in radians per second of a wheel turning at 78.6 rpm Answer to the nearest tenth 78.6 rev 1 min rads min 1 rev 60 sec sec To the nearest tenth
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Now Go the Other Way Change Rads per sec to Revs per min
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Answer to the nearest tenth
Determine the revolutions per minute of a wheel turning at the angular velocity of 33 rads per second Answer to the nearest tenth Our Goal 33 rads revs sec min
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Multiply by a Form of One
Determine the revolutions per minute of a wheel turning at the angular velocity of 33 rads per second Answer to the nearest tenth Our Goal 33 rads 1 rev revs sec min Multiply by a Form of One
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Answer to the nearest tenth
Determine the revolutions per minute of a wheel turning at the angular velocity of 33 rads per second Answer to the nearest tenth Our Goal 33 rads 1 rev revs sec min
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Multiply by a Form of One
Determine the revolutions per minute of a wheel turning at the angular velocity of 33 rads per second Answer to the nearest tenth Our Goal 33 rads 1 rev 60 sec revs 1 min sec min Multiply by a Form of One
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Answer to the nearest tenth
Determine the revolutions per minute of a wheel turning at the angular velocity of 33 rads per second Answer to the nearest tenth 33 rads 1 rev 60 sec revs 1 min sec min To the nearest tenth
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Angular Velocity Problem
More Complicated Angular Velocity Problem
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Find the angular velocity in radians per second when ½ rotation takes 2 minutes to complete
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Find the angular velocity in radians per second when ½ rotation takes 2 minutes to complete
Our Goal rads sec
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Find the angular velocity in radians per second when ½ rotation takes 2 minutes to complete
Our Goal rot 2 rads 2 min 2 sec
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Multiply by a Form of One
Find the angular velocity in radians per second when ½ rotation takes 2 minutes to complete Our Goal ? rot 2 rads 2 min 2 rot sec Multiply by a Form of One
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All the Distance and Time Facts
Known Facts All the Distance and Time Facts
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Find the angular velocity in radians per second when ½ rotation takes 2 minutes to complete
Our Goal rot 2 rads 2 sec 2 min 1 rot
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Multiply by a Form of One
Find the angular velocity in radians per second when ½ rotation takes 2 minutes to complete Our Goal rot 2 rads 1 min 2 min 2 sec 1 rot 60 sec Multiply by a Form of One
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Find the angular velocity in radians per second when ½ rotation takes 2 minutes to complete
1 min rads 2 min 2 1 rot 60 sec sec
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Find the angular velocity in radians per second when ½ rotation takes 2 minutes to complete
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You Try
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Find the angular velocity in radians per second when 3/5 revolution takes 12 minutes to complete
You Try
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Find the angular velocity in radians per second when 3/5 revolution takes 12 minutes to complete
Work Next Page
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Find the angular velocity in radians per second when 3/5 revolution takes 12 minutes to complete
rot 5 1 min rads 12 min 5 1 rot 60 sec sec
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Centimeters per second
Linear Velocity Units of Measure Miles per hour Feet per second Centimeters per second
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How Fast
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How Fast Arc Length In What Period of Time
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Arc Length In What Period of Time
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Arc Length In What Period of Time
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Arc Length In What Period of Time
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Arc Length Divided by
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Velocity Divided by
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Know
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Know
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v is the velocity measured in units of length / units of time
Formula Linear Velocity v is the velocity measured in units of length / units of time r is the length of the radius measured in units of length is the angular velocity measured in radians / units of time
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Find the Linear Velocity in cm/sec for the following
Ex 1 Our Goal cm sec
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Find the Linear Velocity in cm/sec for the following
Ex 1 Our Goal 10 cm cm 1 rad sec Always put the radius in a fraction over 1 radius to use the units of measure to reach Our Goal
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Find the Linear Velocity in cm/sec for the following
Ex 1 Our Goal 10 cm cm 1 rad 1 sec sec
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1 radian gets its definition from 1 radius
Remember has a measure of 1 radian
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Multiply by a Form of One
Find the Linear Velocity in cm/sec for the following Ex 1 Our Goal 10 cm cm 1 rad 1 sec sec Multiply by a Form of One
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Find the Linear Velocity in cm/sec for the following
Ex 1 10 cm cm 1 rad 1 sec sec To the nearest tenth
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Find the Linear Velocity in cm/sec for the following
Ex 2 Our Goal cm sec
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Find the Linear Velocity in cm/sec for the following
Ex 2 Our Goal 15 cm cm 1 rad sec Always put the radius in a fraction over 1 radius to use the units of measure to reach Our Goal
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Find the Linear Velocity in cm/sec for the following
Ex 2 Our Goal 15 cm cm 1 rad sec
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Find the Linear Velocity in cm/sec for the following
Ex 2 Our Goal 15 cm cm 1 rad 1 sec sec
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Find the Linear Velocity in cm/sec for the following
Ex 2 15 cm cm 1 rad 1 sec sec To the nearest tenth
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Linear Velocity Problems
More Complicated Linear Velocity Problems
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute.
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute. What Formula?
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute. What's The Goal? cm sec
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute. ? Where's The cm sec
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute. 72 cm cm 1 rad sec
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute. 72 cm cm 1 rad sec Where's The ?
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We Know
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We Know
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We Know aka
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute.
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute.
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute. 1 min
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute. 1 min
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GO BACK TO THE PROBLEM
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute. Our Goal 72 cm cm 1 rad 1 min sec
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Multiply by a Form of One
Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute. Our Goal 72 cm 1 min cm 1 rad 1 min 60 sec sec Multiply by a Form of One
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Find the Linear Velocity in cm/sec of a point on a circle 72cm from the center that moves through an angle of measure 1.4π in 1 minute. 72 cm 1 min cm 1 rad 1 min 60 sec sec To the nearest tenth
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You Try
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Find the Linear Velocity in cm/sec of a point on a circle 1
Find the Linear Velocity in cm/sec of a point on a circle 1.2m from the center that moves through an angle of measure 250º in 1 minute. You Try To the nearest tenth Sol Next Slide
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See Work on Following Slides
Find the Linear Velocity in cm/sec of a point on a circle 1.2m from the center that moves through an angle of measure 250º in 1 minute. See Work on Following Slides To the nearest tenth
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Find the Linear Velocity in cm/sec of a point on a circle 1
Find the Linear Velocity in cm/sec of a point on a circle 1.2m from the center that moves through an angle of measure 250º in 1 minute. Our Goal 1 min 100 cm cm sec 360º 60 sec 1 m
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Multiply by a Form of One
Find the Linear Velocity in cm/sec of a point on a circle 1.2m from the center that moves through an angle of measure 250º in 1 minute. Our Goal 1.2 m 1 min 100 cm cm 1 rad 1 min 360º 60 sec 1 m sec Multiply by a Form of One
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Multiply by a Form of One
Find the Linear Velocity in cm/sec of a point on a circle 1.2m from the center that moves through an angle of measure 250º in 1 minute. Our Goal 1.2 m 1 min 100 cm cm 1 rad 1 min 180º 60 sec 1 m sec Multiply by a Form of One
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Multiply by a Form of One
Find the Linear Velocity in cm/sec of a point on a circle 1.2m from the center that moves through an angle of measure 250º in 1 minute. Our Goal 1.2 m 1 min 100 cm cm 1 rad 1 min 180º 60 sec 1 m sec Multiply by a Form of One
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Find the Linear Velocity in cm/sec of a point on a circle 1
Find the Linear Velocity in cm/sec of a point on a circle 1.2m from the center that moves through an angle of measure 250º in 1 minute. Our Goal 1.2 m 1 min 100 cm cm 1 rad 1 min 180º 60 sec 1 m sec
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Find the Linear Velocity in cm/sec of a point on a circle 1
Find the Linear Velocity in cm/sec of a point on a circle 1.2m from the center that moves through an angle of measure 250º in 1 minute. 1.2 m 1 min 100 cm cm 1 rad 1 min 180º 60 sec 1 m sec To the nearest tenth
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Summary Units of Measure
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Radius Units of length (cm, m, in, ft, etc)
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Radius Angular Displacement Units of length (cm, m, in, ft, etc)
radians, degrees sometimes rev or rotation
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Radius Angular Displacement Arc Length
Units of length (cm, m, in, ft, etc) Angular Displacement radians, degrees sometimes rev or rotation Units of length (cm, m, in, ft, etc) Arc Length
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Radius Angular Displacement Arc Length Angular Velocity
Units of length (cm, m, in, ft, etc) Angular Displacement radians, degrees sometimes rev or rotation Units of length (cm, m, in, ft, etc) Arc Length Angular Velocity Radians per second or rpm
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Radius Angular Displacement Arc Length Angular Velocity
Units of length (cm, m, in, ft, etc) Angular Displacement radians, degrees sometimes rev or rotation Units of length (cm, m, in, ft, etc) Arc Length Angular Velocity Radians per second or rpm Linear Velocity
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Given a list of a few of the answers from a test on:
Let’s use the Units of Measure to determine what the test was asking for
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1) ft/sec 5) cm 6) 17,223 mi/hr 3) rad/sec 7) 1.44 4) rpm 8) 65
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