Do now: Tūrei, 15 Mahuru 2015 Fun Clips: Awesome Mini Bike Loop Globe of Death Progress test tomorrow: Everything so far: Centre of mass, momentum Circular motion Homework

Today’s Kaupapa: Tūrei, 15 Mahuru )What is the difference between rotational motion and circular motion? 2)What is a radian? 3)Why do we use radians? 4)Converting between radians and degrees

1)Clear your calculator memory 2)Calculate: sin30 o = 3)Calculate: sin -1 (0.7071) = Everyone: Tūrei, 15 Mahuru 2015

Discuss in pairs: Tūrei, 15 Mahuru )What is the difference between rotational motion and circular motion? 2)What is a radian? 3)Why do we use radians?

Three types of motion: 1)Translational (COM moves in straight lines) 2)Circular (COM orbits a central point) 3)Rotational (spinning around the COM)

What is a radian? Great animation: 1) How would you describe this in words? 2) How would you describe this mathematically? Board notes

Radians: In general:  = d / r (or d =  x r) d is the distance travelled around the arc of a circle - measured in metres  is the “angular displacement” - measured in radians A ferris wheel turns through 6 revolutions. a) What is the angular displacement of the wheel? b) What distance does a person riding on the ferris wheel move if the radius is 10m?

Why do we use radians? For rotational motion, displacement d and velocity v depend on the radius of rotation But both points move through the same angular displacement and have the same angular velocity

Board notes Converting between radians and degrees

Angular Velocity Measured in radians per second (rad s -1 ) Symbol  (omega) not w (double u) Average angular velocity = angular displacement time taken

How is the angular velocity  related to the translational speed v?  d = r  v = r  Spot the pattern? 

Example: An aircraft propellor rotates at 4000 rpm (revolutions per minute) and has a radius of 0.80m. Find: a)the angular velocity of the propellor b) the linear speed of the tip of the propellor blade