Name:_________________________Date:_______________________Trigonometry
1.1 Arc Length word problems
1. A phonograph record with diameter 12 inches rotates at 45 rpm. Find the distance that
a point on the rim travels in one minute.
2. An automobile tire with diameter of 2 feet turns 10 times per second. How far does a
point on the tread travel in one minute?
3. A Ferris wheel with diameter of 50 feet makes one revolution every two minutes.
What is the speed of a seat on the rim of the wheel?
4. A merry-go-round 40 feet in diameter makes four revolutions every minute. What is
the speed of a seat on the rim?
5. From an observation point on Earth, the angle subtended by the sun 150,000,000 km
away is about 0.0093 radians. Approximate the diameter of the sun by finding the length
of the arc that is in bold print.
6. The angular speed of the larger pulley wheel shown is 50 rpm. Find the angular speed
and rim speed of the smaller wheel.
6 cm
15 cm
7. A clock pendulum swings back and forth once every two seconds. If its length is one
meter and the greatest angle that it makes with the vertical is 12, how many kilometers
does the bottom end of the pendulum travel in one day?
8. What is the angular speed in radians per second of the hour hand of a clock? If the
hand is 5 cm long, how fast is the tip moving in millimeters per second?
Trignometry
Arc Length Problems
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