Linear speed of an earth satellite and floppy disk?

Question

An earth satellite in circular orbit 1250 kilometers high makes one complete revolution every 90 minutes. What is its linear speed? Use 6400 kilometers for the radius of the earth.

The radius of the magnetic disk in a 3.5-inch diskette is 1.68 inches. Find the linear speed of a point on the circumference of the disk if it is rotating at a speed of 360 revolutions per minute.

Any help at all will be greatly appreciated. You do not need to answer both to be chosen as the best answerer. I know that linear speed = arc length/time & arc length is equal to radius times theta. I'm just not sure how to put it together to get my answer. Please help me.

And to those who game for points, don't tell me to do my own homework. I obviously have hundreds more of these and need help. I didn't ask for someone to do my homework, but specifically for some help. So please, if you're going to put "sfjkfdsl" as an answer, save yourself some time and ignore this question. Thank you& have a nice day.

Answer 1

Hundreds more, huh? You poor thing. LET'S SEE:

Draw a circle. This is the Earth. Draw another circle outside the first circle. This is the orbit of the satellite. Inner radius = 6400 km. Outer radius = 6400 km + 1250 km

Linear speed and angular speed are related by the following equation:
v = omega * r

omega is in radians per second, radians per minute, or whatever. For the satellite,
omega = 1 rev / 90 minutes = 2 pi radians / 90 minutes

Linear speed of satellite:
v = omega * r = [2pi / 90 minutes ] * [1250 km + 6400 km]
Punch that answer and that is it in km/minute. Convert to km/hr or whatever you want.

Second question:

Again,

v = omega * r

omega = 360 rev / min = 360 * 2pi radians / min
r = 1.68 in

v = [360 * 2pi radians / min ] * 1.68 in

again, punch this and get an anser in inches/minute. Convert to whatever.

To convert, use the factor label technique.

360 * 2 pi radians
----------------------- X
minute

60 minutes
-------------------- =
1 hour


"whatever" radians
----------------------------
hour

Good luck!

Answer 2

For the earth satellite:

1) first figure out the circumference of the orbit. The equation is

C = Pi X D

Pi is approximately equal to 3.1416

D is the diameter, which is equal to two times the radius

D = 2 X R

R is the radius

Combining these two equations we get:

C = Pi X 2 X R

So the circumference is 3.1416 X 2 X 6400 = 40,212 miles

The linear speed is the distance, which is the circumference divided by the time:

S = D / T

So the speed is 40,212 / 90 = 446.8 miles per minute.

In the case of the magnetic disk the same basic calculations are required:

C = Pi X 2 X R

So the circumference of the disk is 3.1416 X 2 X 1.68 = 10.56 inches.

The time is expressed a little differently here in that they give you the time for 360 revolutions. To find the time for a single revolution we need to divide the time by the number of revolutions, which is 1 second divided by 360 revolutions:

1 / 360 = .002777 seconds per one revolution

Now we can find the speed:

S = C / T

which is 10.56 / .002777 = 3800 inches per second

Answer 3

Okay, first the satellite.

The radius of the satellite's orbit is 6400+1250 = 7650km, so the length it travels in one orbit is 2*pi*7650 km or approximately 4.807 x 10^7 meters (48,066 km). If the orbital period is 90 minutes = 5,400 seconds then the speed in orbit is 4.807 x 10^7 divided by 5,400 or about 8,900 meters per second, or if you prefer, about 32,040 kilometers per hour.

Second, the FDD:

The radius is 1.68 inches = 4.27 centimeters, so the circumference is 2*pi*4.27 or approximately 26.8 cm. The rotational speed is 360 rpm or 6 revolutions per second, so a point on the edge of the floppy disk travels 26.8 * 6 = 161 cm/s or 1.61 m/s or if you prefer, 5.79 kilometers per hour.

Answer 4

The circle that the satellite makes, has a radius of 7650 km. The circumference of that circle is 2*pi*7650 km = about 48066 km. Therefore it's speed is 48066 km / 90 mins. Which reduces to about 534 KPM.

Same on stuff with the disk. radius = 1.68 in. circumference = 2*pi*1.68 in = 10.556 in.
Now the trick is to figure out how long a single revolution is. You know that it goes at 360 rev / 1 min, so you can flip the fraction to find the time per 1 rev. Which is 1/360 mins.

Speed is 10.556 in / (1/360) mins = about 3800 in. per min. Which if you want to convert to km per min, you times by 2.54 to get cm. and divide by 100 to get meters and divide by 1000 to get km. which yields 0.09652 KPM

The satellite is therefore moving much faster than the edge of the floppy disk.