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# GBK Precalculus Jordan Johnson - PowerPoint PPT Presentation

GBK Precalculus Jordan Johnson. Today’s agenda. Greetings Intro & Lesson: Rotary Motion Classwork / Homework Announcement : Quiz Friday, 3-1 to 3-7. Clean-up. A DVD:. Rotary Motion. As an object rotates, there are multiple velocities:

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GBK Precalculus Jordan Johnson

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## GBK PrecalculusJordan Johnson

### Today’s agenda

• Greetings

• Intro & Lesson: Rotary Motion

• Classwork / Homework

• Announcement: Quiz Friday, 3-1 to 3-7.

• Clean-up

### Rotary Motion

• As an object rotates, there are multiple velocities:

• Angular velocity: the rotation speed in degrees, radians, or revolutions per unit of time.

• Most common example: RPM

• Linear velocity: the distance a point travels (on its arc) per unit of time.

### Rotary Motion

• Equations:

• The angular velocity ω of an objectis the rate of rotation in radians or degrees () over t units of time:

• The linear velocity v of a point is the arc length a traversed in t units of time:

### Conversions:Linear Velocity  Angular Velocity

• If  is an angle in radians and ωis in radians per unit of time, then the linear velocity v and arc length a are given by these equations:

• a = r

• v = rω

### Linear & Angular Velocity

• Audio CDs have a constant linear velocity of 1.2 m/sec.

• Angular velocity is 495rpm at innermost, 212rpm at outermost.

### Other Applications

• Tire/engine rotation

• Gear or sprocket ratios

• Angular velocity of firstgear/sprocket

•  linear velocity (rateof chain/tooth motion)

•  angular velocity ofsecond gear/sprocket

### Classwork / HW:

• For Monday:

• Read Section 3-8 and do:

• Q1-Q10

• Problems 1-9 odd, 10, and 11.

• Bonus:

• Find the angular velocity of the spinning staff, and the linear velocity of the light at its end.

### Clean-up / Reminders

• Pick up all trash / items.

• Push in chairs (at front and side tables).

• See you tomorrow!