© 2010 Pearson Education, Inc. Circular Motion – Section 3.8 (pgs. 89 – 92)

© 2010 Pearson Education, Inc. Background  “The 32 cars on the London Eye Ferris wheel move at a constant speed of about 0.5 m/s in a vertical circle of radius 65 m.”  The cars may move at a constant speed, but they do not move with constant velocity.”  Why not!?  The direction of circular motion is constantly changing.

© 2010 Pearson Education, Inc. Uniform Circular Motion  Constant speed, but continuously changing direction.  (We will discuss some basic ideas about circular motion now, and then get more complicated in Ch. 6)  DEMO!

© 2010 Pearson Education, Inc. Period, Frequency, and Speed  The time interval it takes an object to go around a circle one time, completing one revolution (abbreviated rev), is called the period of the motion.  Period is represented with the symbol T.

© 2010 Pearson Education, Inc. Period, Frequency, and Speed  Rather than specify the time for one revolution, we can specify circular motion by its frequency  The number of revolutions per second  Symbol  f

© 2010 Pearson Education, Inc. For example…  An object with a period of ½ second completes ____ revolutions each second.  An object can make 10 revolutions in 1 s if it’s period is ___________ of a second.  The frequency is the inverse of the period.

© 2010 Pearson Education, Inc. **Note about frequency…  Frequency is often expressed as “revolutions per second” but revolutions are not true units (they’re merely the counting of events)  THUS, the SI unit of frequency is simply inverse seconds, or s -1  Frequency can also be given in revolutions per minute (rpm) or another time interval, but will normally need to be converted to s -1 before doing calculations

© 2010 Pearson Education, Inc. Describing Circular Motion (with Math!)  What distance does the object travel in 1 revolution?  So, we can write an equation relating the period, the radius, and the speed:  And, using the frequency and period relationship, we can simply write: ?

© 2010 Pearson Education, Inc. Example 3.13  An audio CD has a diameter of 120 mm and spins at up to 540 rpm. When a CD is spinning at its maximum rate, how much time is required for one revolution? If a speck of dust rides on the outside edge of the disk, how fast is it moving?  What do we need to do first?  Conversions!

© 2010 Pearson Education, Inc. Example 3.13 cont’d  f = 9.0 s -1 & diameter =.12 m a) How much time is required for one revolution? b) How fast is the speck traveling?

© 2010 Pearson Education, Inc.  Pg. 98 #34 (a-b) and #35 (a-b)

© 2010 Pearson Education, Inc.

Acceleration in Circular Motion  Since the velocity is constantly changing as the direction of motion changes the object in uniform circular motion IS accelerating  Which way does the object accelerate?  Directly toward the center of a circle  Known as centripetal acceleration

© 2010 Pearson Education, Inc. Example

© 2010 Pearson Education, Inc. Circular Motion There is an acceleration because the velocity is changing direction. Slide 3-43

© 2010 Pearson Education, Inc. Deriving the acceleration equation…

© 2010 Pearson Education, Inc. Example  A typical carnival Ferris wheel has a radius of 9.0 m and rotates 6.0 times per minute. What magnitude acceleration do the riders experience? 3.15 (pg. 92)

© 2010 Pearson Education, Inc. Example Problems: Circular Motion Two friends are comparing the acceleration of their vehicles. Josh owns a Ford Mustang, which he clocks as doing 0 to 60 mph in a time of 5.6 seconds. Josie has a Mini Cooper that she claims is capable of higher acceleration. When Josh laughs at her, she proceeds to drive her car in a tight circle at 13 mph. Which car experiences a higher acceleration? Slide 3-44

© 2010 Pearson Education, Inc. Example Problems: Circular Motion Turning a corner at a typical large intersection is a city means driving your car through a circular arc with a radius of about 25 m. If the maximum advisable acceleration of your vehicle through a turn on wet pavement is 0.40 times the free-fall acceleration, what is the maximum speed at which you should drive through this turn? Slide 3-44

© 2010 Pearson Education, Inc. Slide 3-46 Summary