area of a circle sector
angular speed
linear speed
arc length, radius, and theta
Mixed
100
the formula for the area of a sector of a circle
What is theta/2 times r squared
100
The four possible units for angular speed
What is radians/time, degrees/time, revolutions/time, rotations/time
100
One equation for finding linear speed that does not use angular speed
What is arc length/ time or theta divided by time multiplied by radius
100
The arc length (in terms of pi) for a central angle of 75 degrees in a circle whose radius is 4 cm.
What is 5 pi/ 3 or 1.67 pi centimeters
100
linear velocity does this if you increase how far an object is from the point of rotation
What is increases
200
the area of the sector whose central angle is pi/2 radians and whose radius is 4inches (in terms of pi)
What is 4pi
200
The angular speed in radians/min of a fan with 16 inch blades that rotate at 45 rpm (in terms of pi)
What is 90 pi radians
200
How fast a load rises using a winch whose radius is 2 feet and makes 8 revolutions every 15 seconds
What is 6.7 feet/second
200
The amount the tip of a wiper blade will travel (not in terms of pi) if the blade is 24 inches long and sweeps an angle of 120 degrees
What is 50.26 inches
200
Why the unit "radians" sometimes disappears from a calculation
What is because it is a ration of arc length to radius and length/length equals 1
300
The area of a sector whose radius is 8cm and whose central angle is 80 degrees (not in terms of pi).
What is 44.7 square centimeters
300
Angular speed for a wheel that rotates at 50rpm in radians per second (not in terms of pi)
What is 5.23 rad/sec
300
The linear speed in mph of a car whose wheels spin at 600rpm and have a radius of 11 inches. (hint: 5280 ft = 1 mile)
What is 39.25 mph
300
The distance in miles that a car's wheel travels if its diameter is 28 inches and it revolves 10,000 times. (hint: 5280 ft = 1 mile)
What is 13.9 miles
300
the linear velocity for an object at the center of a circle
What is zero
400
The area a cow can eat when it is tethered on a 20 foot rope in the middle of a 60 foot wall (not in terms of pi).
What is 628 square feet
400
The angular speed for a toy racing car on a track that is 2.6 meters in diameter and traveling at 0.5 m/s
What is 0.38 radians/second
400
The linear speed in feet per minute for a pendulum that in 40 inches long and swings through an angle of 18 degrees in 15 seconds
What is 4.2 feet/minute
400
The distance the Earth travels around the Sun (not in terms of pi) if you assume its orbit is a circle whose radius is 93 million miles
What is 584 million miles
400
Why all the people in a "crack the whip" game have the same angular velocity if they keep their arms at 180 degrees
What is they will all go around the center of the circle the same number of times - they will have the same rotations per time
500
An irrigation system uses a straight sprinkler pipe that in 300 feet long and that pivots around a central point. A rock stops the sprinkler when it has pivoted 280 degrees. What area (in feet squared) was watered, use 2 significant figures?
What is 220,000 square feet
500
The angular speed (in radians per hour) of a truck's axle if the truck is traveling 50 mph and it has 48 inch diameter wheels. (hint: 1 mile = 5280 feet)
What is 132,000 rad/hour
500
how fast a plane is moving if a ship's radar that rotates at 15 rpm shows the plane 29.74 miles away (directly northeast of the ship) and then shows the plane 29.12 miles away (directly northeast of the ship) on the next revolution. (give your answer in miles/minute)
What is 9.3 miles/minute
500
The length of the handle (not in terms of pi) that travels 4 inches when it is twisted 1/2 of a turn (assume that the handle will not turn past 90 degrees - this is a "full" turn)
What is 5.1 inches
500
what the wheels on the bus have to do
What is keep the same linear and angular velocities or go 'round and 'round
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