OPENING QUESTIONS: You're on a hike up at Gothic Basin in the Cascades (YAY!) and you drop your Apple Phone between two boulders. Fortunately you've brought along a 2 meter steel pry-bar for just that eventuality. You and your friends give a mighty heave, the boulders part and you reach down and retrieve your unharmed phone.
How is it that your pry bar worked pretty easily, but there was no way at all for you to move the boulders yourself?
OBJECTIVE: I will be able to utilize the relationship between Torque and angular acceleration during today's class.
WORDS FOR TODAY:
FORMULAE & TERMS:
Torque: Force through a displacement (NOT WORK!)
═══════════════════════════
There are a veritable FLOOD of new terms to get comfortable with in this unit... so let's start NOW:
Term
|
Symbol |
Formula
|
SI units
|
Description
|
Notes
|
radian
|
θ |
--- |
radians |
π (in radians) = 180o |
1 radian = 57.3 degrees |
period
|
T |
--- |
seconds |
the period = time for one full rotation |
|
angular speed
|
ω |
∆θ/dt |
radians/sec |
∆θ/dt is instantaneous speed
|
angles ALWAYS described in radians |
angular acceleration
|
α |
dω/dt |
rad/s/s | dω/dt is instantaneous acc | |
tangential velocity
|
vt |
vt = rω |
m/s |
linear velocity at any radial distance "r" |
|
tangential acceleration |
at |
at = rω2 rdω/dt |
m/s/s |
||
centripetal acceleration
|
ac |
ac = v2/r
or rω2 |
m/s2
|
acceleration of an object following a circular path |
Be careful -- radians (by definition) are unit less |
| Torque | τ |
τ=RFsinθ | Nm |
force exerted through displacement (NOT WORK!) | |
I |
depends on shape (see link here) | kgm2 |
The 'pivot point' about which an object rotates. Often associated with center of mass but it does NOT need to be the c.o.m | ||
| This list of equations comes to us from the FINE folks at Georgia State University "Hyperphysics" website | |||||
 |
|||||
WORK O' THE DAY:
Before we begin, let me introduce the annotated bibliography project... let's see how you'd like to modify it as it currently exists.
Let's mix up our groups a bit first...
═══════════════════════════
Grab a meter stick and some free masses. Notice how the amount of effort required to keep the meter stick straight and level (dare I say "Force?") changes as you change the amount of mass and the position of that mass on the meter stick.
Notice also that the meter stick really, REALLY wants to.... what? when you add a mass?
═══════════════════════════
Welcome to the wonderful world of TORQUE!
We use yet another Greek letter (Tau: τ) to represent torque.
We define torque mathematically as τ=RFsinθ
═══════════════════════════
What are the units of Torque? How is torque different from Work? Why do we NOT measure torque in jules? Is the torque mentioned on truck commercials during the Seahawks game as "foot pounds" the same sorta torque that we talk about as Nm?
═══════════════════════════
Please work your way through example 10.3 on page 301.
═══════════════════════════
COURSEWORK: Page 326 (27, 31, 32, 34)
ANSWERS:
═══════════════════════════