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

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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?

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

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

——  ——   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   ———  ———

14 x 540    sec

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

32           1

.

Apr 26, 2020