Pre-Calculus A
Name _________________________________ Hour ______
4.1.2 Worksheet (Day 2)
Arc Length: s = r θ
Angular speed: ω =
θ must be in radians!
Linear speed: v =
𝒔
𝒕
𝜽
𝒕
or
1 rev = 2π rads
𝒓𝜽
𝒕
1) Find each angle in radians
a) 30°
b) 45°
c) 60°
d) 90°
e) 135°
2) Find each angle in degrees
𝒂)
𝝅
b)
𝟔
𝝅
𝟒
c)
𝝅
𝟑
d)
𝝅
𝟐
e)
𝟓𝝅
𝟔
3) Find the arc length on a circle of the given radius and central angle:
Radius
Central Angle________Arc Length?
a)
15 inches
180 degrees
b)
22 feet
60 degrees
c)
27 meters
d) 12 centimeters
𝟐𝝅
𝟑
𝟑𝝅
𝟒
radians
radians
4) A satellite in a circular orbit 1250 kilometers above Earth makes one complete
revolution every 110 minutes. (Assume Earth is a sphere of radius 6400 kilometers)
What is its linear speed?
5) A computerized spin balance machine rotates a 25 inch diameter tire at 480
revolutions per minute.
a) Find the road speed at which the tire is being balanced (convert to miles/hour)
b) What rate should the spin balance machine be set so the tire is being tested for
70 miles per hour?
6) A circular blade on a saw has a diameter of 7.5 inches and rotates at 2400
revolutions per minute.
a) Find the angular speed in radians per second.
b) Find the linear speed of the saw teeth (in feet per second) as they contact
the wood being cut
7) Answers as True or False:
a) A degree is a larger unit than a radian.
b) An angle that measures -1260 degrees lies in Quadrant III
c) The 3 angles in a triangle can have measures of
𝟐𝝅 𝝅
𝟑
, ,
𝝅
𝟒 𝟏𝟐