Unformatted text preview: central angle does it sweep out in 3.1 seconds? Solution: Here we have t = 3.1 sec, ν = 10 m/sec, and r = 4 m. Thus, the angle θ is given by s = r θ ⇒ θ = s r = ν t r = (10 m/sec)(3.1 sec) 4 m = 7.75 rad . In many physical applications angular speed is given in revolutions per minute , abbreviated as rpm . To convert from rpm to, say, radians per second, notice that since there are 2 π radians in one revolution and 60 seconds in one minute, we can convert N rpm to radians per second by “canceling the units” as follows: N rpm = N ✘ ✘ rev ✟ ✟ min · 2 π rad 1 ✘ ✘ rev · 1 ✟ ✟ min 60 sec = N · 2 π 60 rad/sec This works because all we did was multiply by 1 twice. Converting to other units for angular speed works in a similar way. Going in the opposite direction, say, from rad/sec to rpm, gives: N rad/sec = N · 60 2 π rpm...
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 Fall '11
 Dr.Cheun
 Calculus, Frequency, Radian, Revolutions per minute

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