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The Moon orbits the Earth in 27 days - AQA - A-Level Physics - Question 10 - 2022 - Paper 2

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The Moon orbits the Earth in 27 days. What is the angular speed of the Moon's orbit?

Worked Solution & Example Answer:The Moon orbits the Earth in 27 days - AQA - A-Level Physics - Question 10 - 2022 - Paper 2

Step 1

Calculate the orbital period in seconds

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Answer

The orbital period of the Moon is given as 27 days. To convert this to seconds:

27extdays=27imes24imes60imes60extseconds=2,332,800extseconds27 ext{ days} = 27 imes 24 imes 60 imes 60 ext{ seconds} = 2,332,800 ext{ seconds}

Step 2

Determine the angular speed formula

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Answer

Angular speed (ω\omega) can be calculated using the formula:

ω=2πT\omega = \frac{2\pi}{T} where TT is the orbital period in seconds.

Step 3

Apply the formula

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Answer

Now, substituting the orbital period:

ω=2π2,332,800\omega = \frac{2\pi}{2,332,800} Calculating this gives:

ω≈2.7×10−6 rad s−1\omega \approx 2.7 \times 10^{-6} \text{ rad s}^{-1}

Step 4

Select the correct answer

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Answer

The calculated angular speed of the Moon is approximately 2.7×10−62.7 \times 10^{-6} rad s−1^{-1}, which corresponds to option B.

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