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Solving Word Problems Involving Angular Velocity

Updated on April 27, 2011


Solving Problems Involving Angular Velocity


Among the challenging problems I encounter  in Trigonometry are problems involving angular velocity. In this hub, I presented several problems involving angular velocity with their solution.



Problem Number One :


A calesa with wheels whose diameter is 1.5 meters is traveling at 24 kph. Find the angular velocity of the wheel  in revolutions per minute.


Given :


Radius ( r )   =  1.5/2   =   .75 m =è   .75 (1/1000)   =   .00075 km


Linear Velocity (V)  =    24 kph


Angular Velocity (W)  =   ?   in revolution  per minute


V  =   r W =è      W  =   V/r


W  =  (24 km/hr )(1/.00075 km)   =   32,000 radians  per hour


To convert to revolution per minute :


(32,000  rad/hr) (1 rev/2∏) (1 hr/60 min)  = 32,000/376.992   =   84.88



Problem Number Two :


A man was jogging on an oval track with radius  89 meters. If the man was jogging at a speed of 25 m/min, what was the central angle generated by the man after 5   minutes ?


Given :


Radius ( r ) =   89 m


Linear Velocity ( V )  = 25 m/min


Time  ( t )  =   5  minutes


W  =   ө / t        W  =   V/ r


W =  ( 25m/min) ( 1/89m)  =   25/89   rad/ min   =  0.281  rad/min


ө  = Wt


ө  =  (.281 rad/min)  (5 min)  -  1.4 radian


 Convert 1.4 radian to degrees :  ( 1.4 )  ( 180/∏ ) =  80.21 degrees



Problem Number Three :


Suppose a point on a circle with radius  6  cm moves around a circle with angular velocity  of  2∏/5  rad/sec. What is the length of the arc generated after 10 seconds ?


Given :


Radius  ( r )  =  6 cm


Angular Velocity (W )  = 2∏/5  rad/sec


Time ( t )   =  10  seconds


S  =   ?  arc length


V  = r W


    =   (6 cm ) (2) (3.1416)/5   =   7.54  cm/sec


 S  =  Vt   


  S  =  ( 7.54 cm/sec) (10 sec)  =   75.4  cm



Problem  Number  Four :


Find the radius of a pulley which is driven at  10 rev/sec by a belt moving at 10m/sec.


Given :


W =    10  rev/sec


V  =   10  m/sec


Radius  ( r )  =   ?


 R = V/W


W  =  (10 rev/sec) (2 ∏ rad/rev ) = 20 ∏ rad/sec


     r  =   (10m/sec ) /(20 ∏rad/sec)  =  0.16 m



Problem Number Five :


A ferriswheel has a diameter of  10 meters. It is rotating at the rate of  500 m/min. Find its angular velocity in rad/sec.


Radius ( r )  =  10/2  = 5 m


Velocity (V ) = 500 m/min


W  =  ?


W  =   V/r


W  =   (500m/min )/5m  =  100 rad/min


      = (100 rad/min) (1 min/60 sec)  = 100/60 rad/sec  =  1.7 rad/sec



Problem Number  Six :


Find the linear velocity of the tip of the minute hand of a clock if the hand is 7cm

Long ?


V  =  S / t


Given :


Radius  ( r )  =   7cm


W  =  1 rev/hr   =  2∏ rad/hr


V  =  ?


V  =  r W


V  =  (7 cm)  (2∏rad/hr)  =  14 ∏ cm/hr  = ( 14∏/60) cm/min  = .73 cm/min












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    • profile image


      3 years ago

      thank you for posting ...i learn a lot of this...

    • profile image


      4 years ago

      thanks for posting these problems/solutions, was just what i needed to tune up my angular/linear velocity skills for my exam!

    • profile image


      5 years ago

      It is a great solution. Thanks a lot.... I really like maths...

      Ref: linear displacement transmitter


    • profile image


      6 years ago

      more than exccelent help. i thank u so much.

    • profile image

      Ketsi Humphry 

      6 years ago

      Saying thank you is an understatement... keep up. May GOD BLESS YOU ALL for your wonderful work.

    • profile image

      kristal joy borres 

      6 years ago

      parang ang hirap ...but its okey ...........................thanks po...

    • profile image

      Apus Reybee 

      6 years ago

      tnx .. =D

    • profile image

      jay arcinue 

      7 years ago

      thanks a lot.I deserve this problem to learn more about Pysics..

    • profile image


      7 years ago

      U help me and i understand more. Thank you

    • profile image


      7 years ago

      Thanks! But out of curiosity, hablas español?

    • profile image


      7 years ago

      tnx for this post ,it helps a lot

    • profile image


      7 years ago

      numerical: time period of a satellite having 90 min. for one revolution around the earth

    • profile image

      John Baldy 

      7 years ago

      A big thanks for these solve problems. They are really helpful

    • profile image


      7 years ago

      THANKS!!! exams tomorrow ._.

    • profile image


      7 years ago

      wow nice;;'ds s our assignment in trigo';/thank a lot

    • profile image


      7 years ago

      ThankZ...for helping me..undrestand 8 further

      coz, i have 2 render my report and im so glad that i can have something to share 2 ny classmates! ThaNks..

    • profile image


      8 years ago

      wow!! i finally got it. It helped me understand more these kind of problems. Thank you so much. IT helped me a lot. NOw, i'm ready for my exams. Hopefully. :) .

      Thanks and Godbless ^^ :)

    • profile image

      8 years ago

      thank you :D

    • profile image

      Math learner 

      8 years ago

      At last! :D a helpful and understandable problems and solutions! Thanks a lot!! :)

    • profile image


      8 years ago

      all word is good for education base

    • profile image


      8 years ago

      nice,this one are our assignments in trigo.tnx for posting


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