DMS, LINEAR AND ANGULAR SPEED

Transcription

1 DMS, LINEAR AND ANGULAR SPEED Section 4.1A Precalculus PreAP/Dual, Revised /1/ :13 AM 4.1B: DMS, Linear and Angular Speed 1

2 DEGREES MINUTES SECONDS (DMS) A. Written as: D M S B. It can also be written in decimal degree form or degree form C. Make sure it is in degree mode on the calculator D. Boaters use DMS to help track other vestals E. Pilots use DMS to track oncoming planes or assist to land 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 2

3 STEPS IN WRITING IN DECIMAL FORM A. Keep the first digits in degree form B. Label the second number over 60 (how many minutes are there in an hour?) and convert the second number into a decimal form from a fraction form C. Label the third number over 3600 (how many seconds are there in an hour?) D. Add the digits together and label as degrees E. If the given is negative, exclude the negative until the end 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 3

4 EXAMPLE 1 Convert to decimal form. Round to 4 decimal places. Step 1: Keep the first digits in degree form ' + 29'' 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 4

5 EXAMPLE 1 Convert to decimal form. Round to 4 decimal places. Step 2: Label the second number over 60 (how many minutes are there in a hour?) and convert into a decimal 14 14' = = /1/ :13 AM 4.1B: DMS, Linear and Angular Speed 5

6 EXAMPLE 1 Convert to decimal form. Round to 4 decimal places. Step 3: Label the third number over 3600 (how many seconds are there in a hour?) using the calculator and convert it to a decimal 29 29' = = /1/ :13 AM 4.1B: DMS, Linear and Angular Speed 6

7 EXAMPLE 1 Convert to decimal form. Round to 4 decimal places. Step 4: Add the figures together = /1/ :13 AM 4.1B: DMS, Linear and Angular Speed 7

8 EXAMPLE 2 Convert to decimal form. Round to 4 decimal places /1/ :13 AM 4.1B: DMS, Linear and Angular Speed 8

9 YOUR TURN Convert to decimal form. Round to 4 decimal places /1/ :13 AM 4.1B: DMS, Linear and Angular Speed 9

10 STEPS IN WRITING IN DEGREE FORM A. Keep the first digits in degree form B. Multiply the last numbers with the decimal (behind the degrees) by 60 C. Take the decimals from the previous answer in step 2 and multiply by 60 again D. Put them together and label accordingly 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 10

11 Convert to DMS form. EXAMPLE 3 Step 1: Keep the first digits in degree form Step 2: Multiply the last numbers with the decimal (behind the degrees) by.6 (60 degrees/1 minute) /1/ :13 AM 4.1B: DMS, Linear and Angular Speed 11

12 Convert to DMS form. EXAMPLE 3 Step 3: Take the decimals from the previous answer in step 2 and multiply by 60 again (60 seconds/1 minute) = 45" 48 21'45" 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 12

13 Convert to DMS form. EXAMPLE '24.42" 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 13

14 Convert to DMS form. YOUR TURN 43 33'9" 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 14

15 ANGULAR SPEED A. Angular Speed applies to any object or particle that turns; angle through with the point rotates over time (also known as angle rotation) B. Angular Speed Equation: Angle Time = ω = θ t C. 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 D. Leave answers in radian mode 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 15

16 Distance = Rate Time ANGULAR SPEED (ROTATION) Rate = Angular Speed Distance = Time Central Angle Time = 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 16 t

17 EXAMPLE 5 The blades of the wind turbine are 116 feet long. The propeller rotates at 15 revolutions per minute. Find the angular speed. = t = ( revolutions)( 2) = ( 15)( 2) 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 17

18 EXAMPLE 5 The blades of the wind turbine are 116 feet long. The propeller rotates at 15 revolutions per minute. Find the angular speed. = = t = = ( 15)( 2) radians 30 minute 30 radians 1 minute radians 30 minute 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 18

19 EXAMPLE 6 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. = = = t 2( 2 ) 1min rad 4 min ft 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 19

20 YOUR TURN The circular blade on a saw rotates at 4,200 revolutions per minute. Determine the angular speed of radians per second. rad = 140 sec 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 20

21 LINEAR SPEED A. Linear speed applies to any object or particle that moves; distance that the point travels over time (distance) B. Linear Speed Equation: angular speed Arc Length Time = V = rω where ω = θ t is the C. Therefore, Linear Speed is also known as (Radius) * (Angular Speed) D. Leave answers in radian mode 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 21

22 Distance = Rate Time LINEAR SPEED (DISTANCE) Rate = Linear Speed = V = Distance Time r Arc Length Time t V = r 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 22

23 EXAMPLE 7 The blades of the wind turbine are 116 feet long. The propeller rotates at 15 revolutions per minute. Find the linear speed. = V = r t 15 2 ( )( ) 1min 30 rad = 1min 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 23 rad

24 EXAMPLE 7 The blades of the wind turbine are 116 feet long. The propeller rotates at 15 revolutions per minute. Find the linear speed. V V = 30 rad 1min 30 1min = ( 116 ft. ) ft 3480 min 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 24

25 EXAMPLE 8 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? r = = ft / min V V = ( 12) 16 ft = 1min 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 25 r 60min 1hour 24 V = mph; mph 11 1 mile 5280 ft.

26 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. inches V = min 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 26

27 ASSIGNMENT Page all, 59, all (omit 66) 8/1/ :13 AM 4.1B: DMS, Linear and Angular Speed 27