GBK Precalculus Jordan Johnson

1. GBK PrecalculusJordan Johnson

2. Today’s agenda • Greetings • Intro & Lesson: Rotary Motion • Classwork / Homework • Announcement: Quiz Friday, 3-1 to 3-7. • Clean-up

3. A DVD:

4. 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.

5. 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:

6. 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

7. Linear & Angular Velocity • Audio CDs have a constant linear velocity of 1.2 m/sec. • Angular velocity depends on the read head’s position. • Angular velocity is 495rpm at innermost, 212rpm at outermost.

8. 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

9. Classwork / HW: • For Monday: • Read Section 3-8 and do: • Reading Analysis questions • 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.

10. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and side tables). • See you tomorrow!