Section 3.5 Velocities.

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Presentation transcript:

Section 3.5 Velocities

Linear Velocity 𝑣= 𝑠 𝑡 𝑆=𝑙𝑖𝑛𝑒𝑎𝑟 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡=𝑡𝑖𝑚𝑒

Angular Velocity 𝜔= 𝜃 𝑡

Angular Velocity Greek Letter Omega (lowercase) 𝜔= 𝜃 𝑡

Angular Velocity #1: A CD player turns a CD at about 13680˚ in 5 seconds. What is the angular speed of the cd in radians per second?

Linear Velocity and Angular Velocity #2: Example 3 page 157 A bicycle wheel with a radius of 13 inches turns with an angular velocity of 3 radians per second. Find the distance (in feet) traveled by a point on the bicycle tire in 1 minute.

Linear Velocity and Angular Velocity Derivation

Linear Velocity and Angular Velocity 𝑣=𝑟𝜔 𝜔= 𝜃 𝑡 𝑣= 𝑠 𝑡

Linear Velocity and Angular Velocity #3: A record is spinning at the rate of 25 rpm. If a ladybug is sitting 10 cm from the center of the record:

Linear Velocity and Angular Velocity #3: A record is spinning at the rate of 25 rpm. If a ladybug is sitting 10 cm from the center of the record: a) What is the angular velocity of the ladybug? (radians/sec)

Linear Velocity and Angular Velocity #3: A record is spinning at the rate of 25 rpm. If a ladybug is sitting 10 cm from the center of the record: a) What is the angular velocity of the ladybug? (radians/sec) b) What is the speed of the ladybug? (in cm/sec)

Linear Velocity and Angular Velocity #3: A record is spinning at the rate of 25 rpm. If a ladybug is sitting 10 cm from the center of the record: a) What is the angular velocity of the ladybug? (radians/sec) b) What is the speed of the ladybug? (in cm/sec) c) After 20 seconds, how far has the ladybug traveled? (cm)

Linear Velocity and Angular Velocity #3: A record is spinning at the rate of 25 rpm. If a ladybug is sitting 10 cm from the center of the record: a) What is the angular velocity of the ladybug? (radians/sec) b) What is the speed of the ladybug? (in cm/sec) c) After 20 seconds, how far has the ladybug traveled? (cm) d) After 20 seconds, what angle has the ladybug turned through? (radians)

Linear Velocity and Angular Velocity #4: Page 161 Problem #61