Problem Set: Do all calculations on a separate piece of paper 1. The propellers on an average freighter have a radius of 4 feet. At full speed ahead, the propellers turn at 150 revolutions per minute. a) What is the angular velocity in radians per minute? b) What is the velocity in feet per minute at the tip of the blades?

2. Jeffrey puts a rock in his sling and starts whirling it around. He realizes that in order for the rock to reach Casey, it must leave the sling at a speed of 60 feet per second. So he swings the sling in a circular path of radius 4 feet. What must the angular velocity be in order for Jeffrey to achieve his objective? 3. The minute hand of a watch is 1.3 cm long. What is the linear velocity, in cm per second, of the tip of this hand? (Think: Don’t we know how long it takes a minute hand to make 1 revolution?) 4. a) Determine the angular velocity in radians per second of a wheel turning at 350 rpm. b) Determine the number of rpm of a wheel turning 52.8 rad/s. 5. A flywheel mounted on an engine crankshaft has a radius of 6 in. If the engine is running at 2800 rpm, what is the linear velocity of a point on the outer edge of the flywheel in feet per second?

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6. A toy racing car is traveling around a circular track that is 3.2 m in diameter. It is traveling at 0.31 radians per second. a) Find its angular velocity in degrees per minute b) Find its linear velocity in kilometers per hour. 7. A merry-go-round rotates at 3600 degrees per minute. The diameter of its platform is 28 ft. What is the speed in miles per hour of a point on the edge of the platform? (Recall: 5280 ft in a mile). 8. Rick and Kate are riding on a Ferris wheel. Rick observes that is takes 20 seconds to make a complete revolution. Their seat is 25 feet from the axle of the wheel. a) What is their angular velocity in revolutions per minute? Degrees per minute? Radians per minute? b) What is their linear velocity in miles per hour? 9. A cockroach is sitting 4 cm from the center of a Lazy Susan. Unaware of its presence, Phoebe spins the Lazy Susan through an angle of 120°. a) What distance did it travel? b) If Phoebe turns the Lazy Susan 120° in .5 seconds, what is the cockroach’s linear velocity?

10. DJ L-Boogie has a turntable that has two settings, 33 rpm and 45 rpm. A ladybug lands on the turntable when it is on the 33 rpm setting 10 inches from the center. a) What is the linear velocity of the ladybug in inches per second? In miles per hour? b) The cockroach from question 9 is back. (Call an exterminator!) If he lands L-Boogie’s turntable when it is on the 45 rpm setting 3 inches from the center, what is its linear velocity?

More Applications: Do all work on a separate piece of paper. Box all final answers.

Ex. 1: A cylinder with a 2.5 ft. radius is rotating at 120 rpm.

a) Give the angular velocity in rad/sec and in degrees per second

b) Find the linear velocity of a point on its rim in mph.

Ex. 2: A tire with a 9 inch radius is rotating at 30 mph. Find the angular velocity of a point on its rim. Also express the result in revolutions per minute.

Ex. 3: The radius of the Earth is approximately 3963.2 miles. It takes 23 hours, 56 minutes, and 4.1 seconds for the Earth to rotate once on its axis.

a) Find the angular velocity in both radians per hour and degrees per hour at the equator

b) Find the linear velocity at the equator.

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