1. Linear and Angular Speed
Section 4.1A
Precalculus PreAP/Dual, Revised ©2016
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4.1A: Arc Length and Linear and Angular Speed

2. 4.1A: Arc Length and Linear and Angular Speed
Angular Speed applies to any object or particle that turns; angle through with the point rotates over time (also known as angle rotation)
Angular Speed Equation: 𝑨𝒏𝒈𝒍𝒆 𝑻𝒊𝒎𝒆 =𝝎= 𝜽 𝒕
The angular speed of an object traveling in a circular path is the same, regardless of its distance from the center of the circle. When the angular speed of the object stays the same, the linear speed increases as the object moves farther from the center
Leave answers in radian mode
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4.1A: Arc Length and Linear and Angular Speed

3. Angular Speed (Rotation)
Distance = Rate • Time
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4.1A: Arc Length and Linear and Angular Speed

4. 4.1A: Arc Length and Linear and Angular Speed
Example 1
The blades of the wind turbine are 116 feet long. The propeller rotates at 15 revolutions per minute. Find the angular speed.
8/8/2019 8:42 AM
4.1A: Arc Length and Linear and Angular Speed

5. 4.1A: Arc Length and Linear and Angular Speed
Example 1
The blades of the wind turbine are 116 feet long. The propeller rotates at 15 revolutions per minute. Find the angular speed.
8/8/2019 8:42 AM
4.1A: Arc Length and Linear and Angular Speed

6. 4.1A: Arc Length and Linear and Angular Speed
Example 2
A Ferris wheel at a carnival has a diameter of 52 feet. Suppose it turns at a rate of 2 revolutions per minute. Determine the angular speed.
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4.1A: Arc Length and Linear and Angular Speed

7. 4.1A: Arc Length and Linear and Angular Speed
Your Turn
The circular blade on a saw rotates at 4,200 revolutions per minute. Determine the angular speed of radians per second.
8/8/2019 8:42 AM
4.1A: Arc Length and Linear and Angular Speed

8. 4.1A: Arc Length and Linear and Angular Speed
Linear Speed
Linear speed applies to any object or particle that moves; distance that the point travels over time (distance)
Linear Speed Equation: 𝑨𝒓𝒄 𝑳𝒆𝒏𝒈𝒕𝒉 𝑻𝒊𝒎𝒆 =𝑽=𝒓𝝎 where 𝜽 𝒕 is the angular speed
Therefore, Linear Speed is also known as (Radius) * (Angular Speed)
Leave answers in radian mode
8/8/2019 8:42 AM
4.1A: Arc Length and Linear and Angular Speed

9. Linear Speed (Distance)
Distance = Rate • Time
8/8/2019 8:42 AM
4.1A: Arc Length and Linear and Angular Speed

10. 4.1A: Arc Length and Linear and Angular Speed
Example 3
The blades of the wind turbine are 116 feet long. The propeller rotates at 15 revolutions per minute. Find the linear speed.
8/8/2019 8:42 AM
4.1A: Arc Length and Linear and Angular Speed

11. 4.1A: Arc Length and Linear and Angular Speed
Example 3
The blades of the wind turbine are 116 feet long. The propeller rotates at 15 revolutions per minute. Find the linear speed.
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4.1A: Arc Length and Linear and Angular Speed

12. 4.1A: Arc Length and Linear and Angular Speed
Example 4
A merry go round makes 8 revolutions per minute. The horse is traveling with a radius of 12. How fast is the horse going in miles per hour?
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4.1A: Arc Length and Linear and Angular Speed

13. 4.1A: Arc Length and Linear and Angular Speed
Your Turn
The circular blade on a saw rotates at 4,200 revolutions per minute. Find the linear speed where the blade is 6 inches.
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4.1A: Arc Length and Linear and Angular Speed

14. 4.1A: Arc Length and Linear and Angular Speed
Assignment
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4.1A: Arc Length and Linear and Angular Speed