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: ▫ 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 object is 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 ω is 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 depends on the read head’s position. ▫ Angular velocity is 495rpm at innermost, 212rpm at outermost. Other Applications • Tire/engine rotation • Gear or sprocket ratios ▫ Angular velocity of first gear/sprocket ▫ linear velocity (rate of chain/tooth motion) ▫ angular velocity of second gear/sprocket 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. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and side tables). • See you tomorrow!