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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
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Today’s Kaupapa: Tūrei, 15 Mahuru 2015 1)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
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1)Clear your calculator memory 2)Calculate: sin30 o = 3)Calculate: sin -1 (0.7071) = Everyone: Tūrei, 15 Mahuru 2015
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Discuss in pairs: Tūrei, 15 Mahuru 2015 1)What is the difference between rotational motion and circular motion? 2)What is a radian? 3)Why do we use radians?
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Three types of motion: 1)Translational (COM moves in straight lines) 2)Circular (COM orbits a central point) 3)Rotational (spinning around the COM)
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http://d24w6bsrhbeh9d.cloudfront.net/photo/a6w9eB8_460sa.gif What is a radian? Great animation: 1) How would you describe this in words? 2) How would you describe this mathematically? Board notes
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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?
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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
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Board notes Converting between radians and degrees
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Angular Velocity Measured in radians per second (rad s -1 ) Symbol (omega) not w (double u) Average angular velocity = angular displacement time taken
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How is the angular velocity related to the translational speed v? d = r v = r Spot the pattern?
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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
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