Linear and Angular velocity questions (2)? HELP?

Question

Question 1 - Please explain in steps if possible

A bicycle wheel is 30 inches in diameter.
a. To the nearest revolution, how many times will the wheel turn if the bicycle is ridden for 3 miles?
b. Suppose the wheel turns at a constant rate of 2.75 revolutions per second. What is the linear speed in miles per hour of a point on the tire?

Question 2

Low Earth orbiting (LEO) satellites orbit between 200 and 500 miles above Earth. In order to keep the satellites at a constant distance from Earth, they must maintain a speed of 17,000 miles per hour. Assume Earth's radius is 3960 miles.

a. Find the angular velocity needed to maintain a LEO satellite at 200 miles above Earth.
b. How far above Earth is a LEO with angular velocity of 4 radians per hour?
c. Describe the angular velocity of any LEO satellite.

Answer 1

The circumference is
pi*diameter

divide the distance by the circumference
1 mile = 63 360 inches
3*63360/(3.14*30)
=2018 revolutions


2.75 RPM means that the tire covers
2.75*30*3.14 inches per second
covert to mph
=2.75*30*3.14*3600/63360

14.7 mph

2) The radius at 200 miles is
4160 miles
w=v/r
17,000/4160 = radians per hour
or 4.1 rad/hr or
0.00113515 rad/sec

at that rate the centripetal force will equal the gravitational pull
b) we just did 4 rad/ hr

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