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If q  240 rad/s, what are T and f? How many cycles occur in 27 s? 2. If 56 000 cycles occur in 3.5 s, what is q?

Question

If q = 240 rad/s, what are T and f? How many cycles occur in 27 s?

  1. If 56,000 cycles occur in 3.5 s, what is q?
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Solution

  1. To find the period (T) and frequency (f) when angular velocity (q) is given, we use the following formulas:

    T = 2π / q f = 1 / T

    Given q = 240 rad/s, we can substitute this into the formulas:

    T = 2π / 240 ≈ 0.0262 s f = 1 / 0.0262 ≈ 38.17 Hz

    To find out how many cycles occur in 27 s, we multiply the time by the frequency:

    Number of cycles = 27 s * 38.17 Hz ≈ 1030 cycles

  2. To find the angular velocity (q) when the number of cycles and time are given, we use the formula:

    q = 2π * (number of cycles / time)

    Given 56 000 cycles occur in 3.5 s, we can substitute these values into the formula:

    q = 2π * (56 000 / 3.5) ≈ 100 530 rad/s

This problem has been solved

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