Angular velocity the moon rotates once on its axis in 273...

Angular Velocity The Moon rotates once on its axis in 27.3 days. Its radius is $1.74 \times 10^{6} \mathrm{m}.$ a. What is the period of the Moon's rotation in seconds? b. What is the frequency of the Moon's rotation in $\mathrm{rad} / \mathrm{s} ?$ c. What is the linear speed of a rock on the Moon's equator due only to the Moon's rotation? d. Compare this speed with the speed of a person on Earth's equator due to Earth's rotation.

Transcript

00:01 All right, so this question is about the moon.

00:03 And so let's get down the givens and then we can discuss the questions.

00:07 So it rotates on its axis 27 .3 days.

00:11 So then that means its period is 27 .3 days.

00:24 And the radius is 1 .74 times 10 to the 6 meters.

00:43 And then we want the period in seconds.

00:45 And so for a, what we need to do is convert this to 6 meters.

00:48 Seconds so i still do this in the same way i learned how to do in high school chemistry so maybe this is the way you do it too but basically we kind of make this little chart so we want to get it into seconds so one day is 24 hours and then i put the 24 hours up here because that's what i want as a unit and then day down here because it cancels with this day.

01:24 And then now i'm left with hours and then there's 60 seconds and are 60 minutes per hour.

01:31 So then there's 3 ,600 seconds per hour.

01:43 And so then so that now the hour cancels out and i'll cancel the day like i talked about.

01:53 So now we just need to multiply 27 .3 times 24 times 3 ,600.

02:03 And with that, i get, let's see, 1, 2 .36 times 10 to the 6.

02:16 Actually, i can just copy and paste a number seconds.

02:28 So i'll just write that in scientific notation.

02:33 One, two, three, four, five, six.

02:36 I like to just double check on these things.

02:39 So that's 2 .36.

02:43 Six.

02:46 So just keeping three sig figs because the original number had six sigfig seconds.