Chapter 8 Rotational Motion and Equilibrium Rotational motion
Chapter 8. . . Rotational Motion and Equilibrium
Rotational motion vs Circular Motion What is the difference? Rotational motion involves part of the object moving around its center of mass or some other axis of rotation.
There is more rotational motion in the world than linear LINEAR: Start with origin and + direction Wll ANGULAR: Start with reference line and + direction
Defining Angular Position How would you describe the rotational motion of the bicycle tire? 1) Define its angular position (�� ) a. The angle that the tire makes with the reference line b. + angles move counter-clockwise - angles move clockwise c. SI unit is radian (rad)
The Radian An angle can be measured in degrees, or revolutions, 360 degrees = 1 rev, Or radians…. . , but must be expressed in radians to use the formulas that connect linear and rotational quantities such as angular velocity and tangential velocity. 1 radian is the angle= where the length of the circular arc is =to the radius
Radian History Ancient Babylonians noticed that the stars would make a complete circle in one year
Which is why there are 360 degrees in a circle Ancient calendars had 360 days and every month was 30 days. So one day = 1 degree as the constellations turned. . . 360 degrees
If you were a Martian, you might have had 687 degrees in a circle, since that is their calendar year
A more mathmatically pure measurement, one not based on astronomy, was created in the 1700 s The radian is universal. . . no matter where in the universe it is used, the radian is the same
Radian Activity With your shoulder partner you will complete an investigative activity regarding radians. You will need 1 piece of chalk Meter stick String Calculator And a protractor You may want to remember this song: Twinkle, twinkle little star, Circumference equals 2�� r
We start with a unit circle=a radius of 1 unit
Converting from Degrees to Radians (dimensional analysis) 1) Remind yourself of the relationship of 1 revolution 2�� radians = 360 degrees 2) Simplify. . . use the ½ trick �� radians = 180 degrees Example: How many degrees are there in 1 radian? 1 radian = 180 degrees �� = 57. 3 degrees
Degrees to Radians 1) 30 degrees Your turn. . . 45 degrees 2) 30 degrees • X radians degree 60 degrees 3) �� radians = 180 degrees 4) 30 degrees • �� radians 180 degrees 30�� = 1�� = �� radians 180 6 6 90 degrees 270 degrees
Answers 30 degrees �� /6 radians 45 degrees �� /4 radians 60 degrees �� /3 radians 90 degrees �� /9 radians 180 degrees �� radians 270 degrees 3�� /2 radians
Revolutions to Radians 1) Remind yourself of the relationship of 1 revolution = 2�� radians Example: How many radians are there in 2. 5 revolutions? 2. 5 revolutions= X radians Revolutions 2. 5 rev • 2�� radians 1 rev = 5�� radians
Converting from Radians to degrees 1) Remind yourself of the relationship of 1 revolution 2�� radians = 360 degrees 2) Simplify. . . use the ½ trick �� radians = 180 degrees Example: How many radians are there in 1 degree? 1) �� radians = 1 degree 180
New symbols to learn for angular (turning) motion �� Acceleration �� Velocity θ X, displacement radian
Linear vs Rotational Chart Copy off board… Page 275 #19 If a bowling ball is rolling along the lane, using angular and linear motion, you could calculate how far it travelled (linear) by how many times it rotated G U E S S
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