6.1.4 – angular speed, linear speed. previously, we talked about the arc-length for a portion of...

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6.1.4 – Angular Speed, Linear Speed

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Page 1: 6.1.4 – Angular Speed, Linear Speed. Previously, we talked about the arc-length for a portion of any given circle; AL = r(θ) – Like a distance But, say

6.1.4 – Angular Speed, Linear Speed

Page 2: 6.1.4 – Angular Speed, Linear Speed. Previously, we talked about the arc-length for a portion of any given circle; AL = r(θ) – Like a distance But, say

• Previously, we talked about the arc-length for a portion of any given circle;

• AL = r(θ)– Like a distance

• But, say we want to determine how fastan object is travelingon said arc

Page 3: 6.1.4 – Angular Speed, Linear Speed. Previously, we talked about the arc-length for a portion of any given circle; AL = r(θ) – Like a distance But, say

Angular Speed

• Angular Speed (frequency) = rate of travel along a circle’s circumference– Angle traveled over some time period

• Angular Speed = ω Angle = θ Time = t

• ω = t

Page 4: 6.1.4 – Angular Speed, Linear Speed. Previously, we talked about the arc-length for a portion of any given circle; AL = r(θ) – Like a distance But, say

• Example. A motorcycle wheel has a radius of 18 inches. The wheel travels at 150 rotations per minute. Find the angular speed of the wheel in inches per second. – 2π radians = 1 revolution

Page 5: 6.1.4 – Angular Speed, Linear Speed. Previously, we talked about the arc-length for a portion of any given circle; AL = r(θ) – Like a distance But, say

• Example. A gear has a radius of 3 inches and spins at 2500rpm.

• A) Find the angular speed of the gear in rad/min.

• B) Find the angular speed of the gear in rad/sec.

Page 6: 6.1.4 – Angular Speed, Linear Speed. Previously, we talked about the arc-length for a portion of any given circle; AL = r(θ) – Like a distance But, say

Linear Speed

• Typically, we will talk about the linear speed of a particular object

• Linear Speed = the speed as if an object were traveling in only a linear direction

• Linear Speed = v Radius = r• v = rω

Page 7: 6.1.4 – Angular Speed, Linear Speed. Previously, we talked about the arc-length for a portion of any given circle; AL = r(θ) – Like a distance But, say

• Example. An exercise bike is ridden such that it completes 85 revolutions per minute. A sensor is placed on the wheel such that the radius is 10 inches. – A) Find the angular speed in rad/minute – B) Find the linear speed in feet/minute

Page 8: 6.1.4 – Angular Speed, Linear Speed. Previously, we talked about the arc-length for a portion of any given circle; AL = r(θ) – Like a distance But, say

• Example. The earth takes about 23 hours and 56 minutes to complete on rotation on its’ axis. If the radius of earth is about 6370 KM, what is the linear speed in km/h of a person standing on the equator? – 56 minutes -> hour

Page 9: 6.1.4 – Angular Speed, Linear Speed. Previously, we talked about the arc-length for a portion of any given circle; AL = r(θ) – Like a distance But, say

• Assignment• Pg. 468• 81-84, 94-96

Page 10: 6.1.4 – Angular Speed, Linear Speed. Previously, we talked about the arc-length for a portion of any given circle; AL = r(θ) – Like a distance But, say

• Arc Length = rϴ

• Angular Speed (ω) = ϴ/t

• Linear Speed = v = rω

• Sector Area =

• Pythagoren Theorem: a2 + b2 = c2

2

2r

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