Test Objectives
  • Demonstrate the ability to solve linear speed word problems
  • Demonstrate the ability to solve angular speed word problems
Linear & Angular Speed Practice Test:

#1:

Instructions: Solve each word problem.

a) A satellite traveling in a circular orbit 1,600,000 meters above the surface of the earth takes 7200 seconds to complete an orbit. If the radius of the earth is approximately 6,400,000 meters, what is the linear speed of the satellite in kilometers per hour (kph)? Round your answer to the nearest tenth.


#2:

Instructions: Solve each word problem.

a) A local shop has a machine with a pulley of radius 0.1296 meters. If it takes 36 seconds for 112 centimeters of belt to go around the pulley, what is the angular speed of the pulley in radians per second? Round your answer to the nearest hundredth. Hint: recall that θ = s/r. Also, give the linear speed of the belt in centimeters per second? Round your answer to the nearest tenth.


#3:

Instructions: Solve each word problem.

a) A wind turbine blade with radius 35 feet makes 360 revolutions per hour. Find the linear speed in feet per minute of the wind turbine blade. Round your answer to the nearest tenth.


#4:

Instructions: Solve each word problem.

a) The propellers on a Cessna small-passenger plane have a diameter of 8 feet. At full throttle, the propellers turn at a rate of 9000 revolutions per hour. What is the linear speed in feet per minute at the tip of the blades? Round your answer to the nearest tenth.


#5:

Instructions: Solve each word problem.

a) At the local fair, Jacob is trying to win a rock toss contest. Contestants must place the rock in a sling and whirl it around before releasing. Jacob determines that the rock must leave the sling at a speed of 60 feet per second in order to win. Based on his arm length, the maximum radius of the circular path generated by the sling is 4 feet. What angular speed does Jacob need to obtain in order to win? Give your answer in radians per second. Hint: we know the linear speed.


Written Solutions:

#1:

Solutions:

a) 25,132.7 kph


#2:

Solutions:

a) Angular speed: 0.24 radians/sec, Linear speed: 3.1 cm/sec


#3:

Solutions:

a) 1319.5 ft/sec


#4:

Solutions:

a) 3770 ft/min


#5:

Solutions:

a) 15 radians/sec