# Solving Word Problems Involving Angular Velocity

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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## Comments 21 comments

.. 6 years ago

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

jamali 6 years ago

all word is good for education base

Math learner 6 years ago

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

6 years ago

thank you :D

jeM_33 6 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 ^^ :)

Fmaesheal 5 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..

daski 5 years ago

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

RimaTheOtaku 5 years ago

THANKS!!! exams tomorrow ._.

John Baldy 5 years ago

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

varinder 5 years ago

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

^_^ 5 years ago

tnx for this post ,it helps a lot

:) 5 years ago

Thanks! But out of curiosity, hablas español?

Sahabi 5 years ago

U help me and i understand more. Thank you

jay arcinue 4 years ago

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

Apus Reybee 4 years ago

tnx .. =D

kristal joy borres 4 years ago

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

Ketsi Humphry 4 years ago

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

rogers 3 years ago

more than exccelent help. i thank u so much.

jupeter41 3 years ago

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

Ref: linear displacement transmitter

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http://www.jupiterelectronics.com/

notaek 2 years ago

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

vash 18 months ago

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

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