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I have the question "A washing machine runs its spin cycle at 800 rpm(revolutions per minute). What is the frequency and the angular velocity of the machines drum?"

I know that frequency is 1/T where T is the period. So I multiplied 800 by 60 to get 48000 seconds.

So for frequency I got 2.1 x 10^-5 hz and for angular velocity I got 1.3 x 10^-4 radians per second.

I am not sure if this is correct though.

Dan
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    $800$ rpm means that for each minute that passes, the drum does $800$ full revolutions. How many revolutions can it then do in a single second? – Arthur Nov 30 '16 at 14:21
  • Is it 800/60 ? So 13.3 ? Is this correct ? – Dan Nov 30 '16 at 14:23
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    Yes, that's exactly it. $13.3$ revolutions per second. Which makes the period equal to...? – Arthur Nov 30 '16 at 14:24
  • 0.075 so 0.1 hz ? – Dan Nov 30 '16 at 14:25
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    $0.075$ is correct. But $Hz$ is the unit of frequency ("how many things happen each second?"). Periods are measured in seconds ("how much time does one thing take?"). – Arthur Nov 30 '16 at 14:26
  • But it is asking for the frequency which is 1/T which is 1/13.3 so would it not 0.075 hz ? – Dan Nov 30 '16 at 14:29
  • The frequency is $13,3 Hz$ so the period is $0,075 s$ – MattG88 Nov 30 '16 at 14:49
  • Is it not the frequency which is 0.075 hz and the period which is 1/0.075 which is 13.3 seconds as the frequency f = 1/T which is 1/13.3 which is 0.075 hz and the period T = 1/f which is 1/0.075 which is 13.3 seconds. – Dan Nov 30 '16 at 14:54

2 Answers2

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"A washing machine runs its spin cycle at $800rpm$"...$800rpm$ it is just a frequency but not in standard units, so we have: $800rpm={800\over min}=\frac{800}{60s}\approx13,3s^{-1}=13,3 Hz$. The period will be $T={1\over f}={1\over 13,3 Hz}=0,075 s$.

What about $\omega$?

$\omega={2\pi\over T}\approx 83,78 rad/s$

MattG88
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Frequency is nothing else but the same which is given in the question. It is $800$ rpm, but remember whenever you give you give your answer keep it in standard units. So, the frequency will be $800/60= (40/3) Hz$.

Now, the angular velocity is given by $w=2\pi v$ where v is frequency. Just put the value of frequency in $w=2\pi v$ and get the angular velocity.

Vidyanshu Mishra
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