Review problems
Name ________________-_
1.
A frequent problem in surveying city lots and rural lands adjacent to curves of highways
and railways is that of finding the area when one or more boundary lines is the arc of a
circle. Find the area of the lot shown in the figure. (Source: Anderson, J. and E. Michael,
Introduction to Surveying, Mc-Graw-Hill, 1985)
2.
Nautical miles are used by ships and airplanes. They are different from statute miles, which
equal 5280 ft. A nautical mile is defined to be the arc length along the equator intercepted
by a central angle AOB of 1 minute, as illustrated in the picture. If the equatorial radius of
Earth is 3963 miles, use the arc length formula to approximate the number of statute miles
in 1 nautical mile. Round your answer to two decimal places.
3.
The speedometer of Terry’s small pick-up truck is designed to be accurate with tires of
radius 14 in. Find the number of rotations of a tire in 1 hour if the truck is driven at 55 mph.
Suppose that oversize tires of radius 16 in are placed on the truck. If the truck is now driven
for 1 hour with the speedometer reading 55 mph, how far has the truck gone? If the speed
limit is 55 mph, does Terry deserve a speeding ticket?
Angular and Linear Speed
4. What is angular speed of the hour hand of a clock in radians per hour?
5. What is speed (in mm/sec) of the tip of the second hand of a clock, if the hand is 28 mm
long?
6. A 90-horsepower outboard motor at full throttle will rotate its propeller at 5000 revolutions per
min. What is the angular speed of the propeller in radians per second?
7. The tires of a bicycle have a radius of 13 inches and are turning at a rate of 200 revolutions
per minute. How fast is the bicycle moving in miles per hour?
8. Mars rotates on its axis at a rate of about .2552 radian per hour. Approximately how many
hours are in a Martian “day” (1 rotation)?
9. Earth travels about the sun in an orbit that is almost circular. Assume that the orbit is a circle
with radius 93,000,000 mi. It’s angular and linear speeds are used in designing solar-power
facilities.
a) Assuming that year is 365 days, find the angle in degrees formed by Earth’s movement
in one day to three decimal places.
b) Give the angular speed in degrees per week to three decimal places.
c) Find linear speed of Earth in miles per hour.
10. Earth revolves on its axis once every 24 hours. Assuming that Earth’s radius is 6400 km, find
the following.
a) angular speed of Earth in radians per hour and degrees per hour.
b) linear speed at the North Pole and South Pole in km/hour
c) linear Speed at Quito, Ecuador, a city on the equator in km/hour
d) BONUS: linear speed at Salem, Oregon (halfway from the equator to the North Pole)
11. Two pulleys have radii 15 cm and 8 cm, respectively. The larger pulley rotates 25 times in 36
sec. Find the angular speed of each pulley in radians per second and degrees per second.
12. A thread is being pulled off a spool at a rate of 59.4 cm per sec. Find the radius if the spool if
it makes 152 revolutions per min.
13. A railroad track is laid along the arc of a circle of radius 1800 feet. The circular part of the
track subtends a central angle of 40 . How long (in seconds) will it take a point on the train
traveling 30 mph to go around this portion of the track?
14. The shoulder joint can rotate at about 25 radians per sec. If a golfer’s arm is straight and the
distance from the shoulder to the club head is 5 ft, estimate the linear speed of the club
head from shoulder rotation in miles per hour. Round to the nearest whole number.
(Souce: Cooper, J. and R. Glassow, Kinesiology, Second Ediition, C.V. Mosby, 1968).
Linear and Angular speed
1. The cities of Spokane, WA and Jordan Valley, OR are located approximately on the same north-south
line of longitude. The latitude of Jordan Valley has latitude of 43N, and the cities are 560 km apart.
Find the latitude of Spokane. Use 6400 km for the radius of the earth. Round to the nearest degree.
2. The wheels on a car each have a 15-inch radius. How many revolutions have the wheels each made
if the car travels exactly 1 mile? Answer to the nearest revolution.
3. The tires of a bicycle have a radius of 14 in long and are turning at a rate of 250 revolutions per
minute. How fast is the bicycle moving in miles per hour? Round your answer to the nearest tenth.
4. According to the website http://hyperphysics.phy-astr.gsu.edu/hbase/solar/soldata2.html#c2, the
planet Venus has the most circular orbit of any planet. Find the linear speed (in km/hr) of Venus as it
orbits the sun if it takes 224.7 “Earth” days to make a complete orbit if the radius of the orbit is
108,200,000 kilometers. Use 4 significant digits in your answer.
5. An engineer named Notso Bright (who failed both Trig and Physics) is designing a Ferris Wheel ride.
He wants it to have a radius of 120 feet and make 6 complete rotations in one minute. Find the linear
speed (in miles per hour) of riders on Notso Bright’s ride. Round to the nearest whole number. (Drawing
by Andrew Zesiger)
6. A tricycle has a large wheel in the front and two smaller wheels in the back. The larger wheel has a
radius of 8 inches and the radius of the smaller wheels is 3.25 inches. If Mrs. Gerrish’s son Timothy
rides the tricycle so that the front wheel rotates 15 times in 10 seconds, at what speed does the
smaller wheel rotate in rotations per second? Also, how fast is he traveling in miles per hour? Round
each answer to the nearest tenth.
ANSWERS:
1) 1900 yd2 2) 1.15 mi
3) a. 39, 616 rotations b. 62.9 mi

4)
radian per hour
5) 2.9 mm/sec
6) 523.6 radians/sec
7)15.5 mph
6
8) 24.62 hour
9) a. .986
b. 6.904 per week c. 66,700 mph

10) a.
radian/hr
b. 0 km/hr
c. 1676 km/hr
d. 1200 km/hr
12
11) Larger Pulley: 4.36 radians/sec; 250 /sec Smaller Pulley: 8.18 radians/sec; 469 /sec
12) 3.73 cm 13) 29 sec 14)85 mph
ANSWERS:
Linear and angular speed
1)
N
2) 672 revolutions
6) 3.7 rot/sec and
4.3 mi/h
3) 20.8 mi/h
4) 126,100 km/hr
5) 51 mi/ h