OBJECTIVE:  

1) I will be able to sketch the differences between angular speed and tangential velocity after today's class.

WORDS FOR TODAY:

• centrifugal acceleration (inaccurate)
• centripetal acceleration (accurate but misleading)
• tangential velocity (flying off the disk (meters/second))
• angular speed (internal rotation (radians/second)

FORMULAE:

There are a veritable FLOOD of new terms to get comfortable with in this unit... so let's start NOW:

WORK O' THE DAY: 

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We will be discussing two types of velocities:

1) The Tangential Velocity (visualize flying off into space from the EDGE of a rotating object) or LINEAR Velocity speed in LINEAR TERMS at ANY radius (r), not just from the edge of the rotating object.

2) The Angular speed (how much an angle θ changes with respect to time)

Let's see if *THIS* will help

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Let's take a look at the first two homework problems (on the board please)

And then I will quickly discuss the tangential/radial acceleration problems.

NOTE: it may not be as obvious as it should be but this particular section deals with the unique case of NONuniform acceleration:

1) radial acceleration occurs when the direction changes (so far so good)

2) tangential acceleration occurs ONLY when the speed is changing (notice: speed, not velocity)

MOST of our work to come will be concerned with uniform circular motion (direction is constantly changing but the tangential/linear velocity will be constant)

Soo... where do we need to be now, at this moment:

You should be VERY comfortable with these:

1) 2π (in radians) = 360^o so 1 radian = 53 degrees

2) θ is the angle in question from the center of a rotating object and is ALWAYS measured and/or used in radians. (That means turn every angle in degrees into angles in radians)

3) ω = angular speed measured in radians/sec.

The conversion factor into linear terms is: v = ωr

4) a_c = rω²: centripetal acceleration is ALWAYS directed towards the center of a rotating object

• The linear conversion is a_c = v²/r

Consider this:

1) measure the rate of rotation of the space station

2) calculate the angular speed of the rotation of the space station

3) recall the relationship between centripetal acceleration and angular speed:

a_c = rω²

4) assuming our calculation for the rotation of the space station is fairly accurate, how long would the radial arms of the space ship have to be in order to approximate gravity here on Earth?

5) Let's take another look at the video... did the producers of 2001 get THAT part of the science right?

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Let's spend a few minutes doing just plain, good ol' fashion memorizing drills:

Work with your partners to quiz each other on the basics (as outlined above)

We'll have a gentle competition shortly

Finally, I have a shout out to one of our most gracious and humble colleagues who has gone above and beyond in his preparations for this class (Mrs Fischer tells me he stopped by for guidance on those NASTY c.o.m. integration problems... MOST OUTSTANDING

If time permits, let's try a few more basic rotational dynamics problems:

#35

and also this (and here's one that is LESS successful):

assuming that the radial arm of the simulator was 5 meters long, what is the LINEAR velocity of the simulator when the pilot hits 9 g's?

HOMEWORK:

Read section 6.1 and do example problems 6.1 and 6.2