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A point on a wheel moves at  32π/9 radians per minute.

How many seconds are required for the point to complete 7 revolutions?

Enter your answer, rounded to the nearest tenth,

 Apr 26, 2020
 #1
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32pi/9  R/min   /  60 sec/min  = .186168 R/sec

 

7 rev = 14 pi Radians

 

14 pi R / .186168 R/sec =   236.25 sec

 Apr 26, 2020
 #2
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+1

 

A point on a wheel moves at  32π/9 radians per minute.

How many seconds are required for the point to complete 7 revolutions?

Enter your answer, rounded to the nearest tenth,

 

Convert rotation speed to radians per second            32 π   rad        1    min          32 π     rad 

                                                                                    ——  ——   x   —  ——   =   ———  ——  

                                                                                      9      min       60   sec           540     sec 

 

1 revolution equals 2 π radians, so 

7 revolutions equals 14 π radians,

and the question becomes how long

does it take to turn 14 π radians                                              distance      (the distance is 14 π radians) 

                                                                                     time  =  ———— 

                                                                                                    rate          (the rate is the rad/sec determined above) 

 

To divide by a fraction, you invert 

the divider and multiply.                                                             14  π    radians        540       sec 

Note that π and radians cancel                                      time  =  —–—   ———   x   ———  ——— 

                                                                                                      1          1             32  π    radians   

 

 

                                                                                                     14 x 540    sec

                                                                                        time  =  ——–——  ——   =  236.25 sec rounds to 236.2 sec 

                                                                                                          32           1 

.  

 Apr 26, 2020

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