Angular Velocity Linear Velocity

Review Angular Displacement ARC LENGTH Known Facts

Angular Displacement Definition

ARC LENGTH

All the Distance and Time Facts Known Facts All the Distance and Time Facts

Angular Velocity How Fast

What Angle Did It Move Through In What Period of Time

What Angle Did It Move Through Angular Displacement In What Period of Time

What Angle Did It Move Through Angular Displacement Time In What Period of Time

What Angle Did It Move Through Angular Displacement Time In What Period of Time

Angular Velocity omega omega

Angular Velocity Formula is angular velocity measured in radians per unit of time

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

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

Example Find the angular velocity in radians per second of a wheel turning at 100 rpm

Example Find the angular velocity in radians per second of a wheel turning at 100 rpm Our Goal rads sec

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

Example Find the angular velocity in radians per second of a wheel turning at 100 rpm 100 rev rads min sec

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

All the Distance and Time Facts Known Facts All the Distance and Time Facts

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

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 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

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

You Try

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

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

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

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

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

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

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

Now Go the Other Way Change Rads per sec to Revs per min

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

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

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

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

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

Angular Velocity Problem More Complicated Angular Velocity Problem

Find the angular velocity in radians per second when ½ rotation takes 2 minutes to complete

Find the angular velocity in radians per second when ½ rotation takes 2 minutes to complete Our Goal rads sec

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

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

All the Distance and Time Facts Known Facts All the Distance and Time Facts

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

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

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

Find the angular velocity in radians per second when ½ rotation takes 2 minutes to complete

You Try

Find the angular velocity in radians per second when 3/5 revolution takes 12 minutes to complete You Try

Find the angular velocity in radians per second when 3/5 revolution takes 12 minutes to complete Work Next Page

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

Centimeters per second Linear Velocity Units of Measure Miles per hour Feet per second Centimeters per second

How Fast

How Fast Arc Length In What Period of Time

Arc Length In What Period of Time

Arc Length In What Period of Time

Arc Length In What Period of Time

Arc Length Divided by

Velocity Divided by

Know

Know

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

Find the Linear Velocity in cm/sec for the following Ex 1 Our Goal cm sec

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

Find the Linear Velocity in cm/sec for the following Ex 1 Our Goal 10 cm cm 1 rad 1 sec sec

1 radian gets its definition from 1 radius Remember has a measure of 1 radian

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

Find the Linear Velocity in cm/sec for the following Ex 1 10 cm cm 1 rad 1 sec sec To the nearest tenth

Find the Linear Velocity in cm/sec for the following Ex 2 Our Goal cm sec

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

Find the Linear Velocity in cm/sec for the following Ex 2 Our Goal 15 cm cm 1 rad sec

Find the Linear Velocity in cm/sec for the following Ex 2 Our Goal 15 cm cm 1 rad 1 sec sec

Find the Linear Velocity in cm/sec for the following Ex 2 15 cm cm 1 rad 1 sec sec To the nearest tenth

Linear Velocity Problems More Complicated Linear Velocity Problems

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.

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?

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

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

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

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 ?

We Know

We Know

We Know aka

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.

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.

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

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

GO BACK TO THE PROBLEM

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

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

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

You Try

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

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

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

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

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

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

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

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

Summary Units of Measure

Radius Units of length (cm, m, in, ft, etc)

Radius Angular Displacement Units of length (cm, m, in, ft, etc) radians, degrees sometimes rev or rotation

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

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

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

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

1) 15.6 ft/sec 5) 14.7 cm 6) 17,223 mi/hr 3) 0.16 rad/sec 7) 1.44 4) 11.62 rpm 8) 65