WEBVTT

00:00:00.000 --> 00:00:02.840
This is Giancoli Answers
with Mr. Dychko.

00:00:03.960 --> 00:00:06.720
To convert rpm into radians
per second,

00:00:06.720 --> 00:00:11.600
I find it helpful to remember that rpm is
revolutions per minute

00:00:11.600 --> 00:00:15.840
and writing it this way: rev's
with a division sign 'per'

00:00:15.900 --> 00:00:17.320
and minutes on the bottom

00:00:17.480 --> 00:00:18.800
and then we can see that

00:00:18.800 --> 00:00:22.400
if we write 1 minute for every 60 seconds
the minutes will cancel

00:00:22.500 --> 00:00:26.380
and we can multiply by 2<i>π</i> radians—
one full circle, in other words—

00:00:26.380 --> 00:00:27.620
for every revolution

00:00:27.620 --> 00:00:31.320
and the revolution's cancel leaving us
with radians per second.

00:00:31.780 --> 00:00:37.960
So 7200 times 2<i>π</i> divided by 60
gives 750 radians per second.

00:00:38.680 --> 00:00:41.280
The linear speed of a point

00:00:41.280 --> 00:00:44.460
directly underneath the reading head
when it's positioned

00:00:44.460 --> 00:00:48.240
3 centimeters from the center of
the hard drive platter

00:00:48.460 --> 00:00:52.840
will be 3 times 10 to the minus 2 meters—
converting that centimeters into meters—

00:00:53.000 --> 00:00:57.800
times by the angular velocity of
the platter which is

00:00:57.800 --> 00:01:00.220
753.98 radians per second

00:01:00.280 --> 00:01:01.840
and that gives linear speed

00:01:01.840 --> 00:01:05.200
of a point right under the reading head of
23 meters per second;

00:01:05.340 --> 00:01:07.740
notice how I use the unrounded number

00:01:07.740 --> 00:01:11.300
in the calculation to avoid intermediate
rounding error.

00:01:11.780 --> 00:01:14.020
And then if there's a writing head

00:01:14.080 --> 00:01:18.120
positioned there and it can write 1 bit

00:01:18.120 --> 00:01:21.180
for every 0.5 micrometers
where I have written

00:01:21.180 --> 00:01:23.700
0.5 times 10 to the minus 6 meters here

00:01:23.860 --> 00:01:25.420
and then times that by

00:01:25.420 --> 00:01:29.220
the speed that the point underneath
the writing head is going—

00:01:29.220 --> 00:01:32.340
linear speed, 22.619 meters per second—

00:01:32.420 --> 00:01:34.160
the meters cancel and we get

00:01:35.040 --> 00:01:39.180
4.5 times 10 to the 7 bits per second.