OPENING QUESTIONS:
1) Explain the key to solving the ferris wheel problem to your group. Make sure you understand why we use mv2/r to describe the resulting motion of the person, but we do NOT include it in the sum-of-the-forces part of the equation.
2) If a space station completes one revolution in 23.5 seconds to simulate 1.00 g of acceleration on Earth, what is the circumference of the space station?
═══════════════════════════
OBJECTIVE:
I will be able to solve basic circular motion problems during today's class.
WORDS FOR TODAY:
- centrifugal motion (inaccurate)
- centripetal motion (center-seeking)
- period (time for one revolution)
- angular velocity = ω = radians/sec
- linear velocity = rω =(meters)(rad)/(sec) = m/sec
- angular acceleration = α = radians/sec2
- linear acceleration = rω2 = (meters)(rad2)/(sec2) = m/sec2
FORMULAE OBECTUS:
centripetal acceleration: ac = v2/r
period: T = 2πr/v
angular speed: ω=2π/T (radians/sec)
tangential velocity: v = rω (meters/sec)
tangential acceleration: a = rω2 (meters/sec2) = rα
WORK O' THE DAY:
Ooops... we were supposed to do this *yesterday*
Let's talk extra practice:
MC once/twice a week? FR once per week?
═══════════════════════════
Let's take a step back for a moment.... (I think we may be getting buried by terms, so let's do a K.I.S.S. anaylsis:
ALL OF THE FOLLOWING ASSUMES UNIFORM CIRCULAR MOTION.
1) Rotational speed can be measure in meters/sec (how far an object moves in a circular fashion per second)
2) Rotational motion can also be measure in radians/sec (how much an angle changes) and in this case it is called angular speed and represented by the symbol ω.
3) We are frequently interested in the tangential velocity of a rotating object. I tend to think of that as if a bug was sitting at the edge of a rotating wheel. If the wheel stops moving suddenly, the bug will be launched off in a tangential, linear fashion with a particular speed in m/s that we abbreviate as vt
4) We are also frequently interested how much the tangential velocity changes, we call that tangential acceleration (at) and also measure that in m/s.
5) If we want to know how much the angular velocity is changing per second, we call that the angular acceleration and use the symbol α.
6) Centripetal acceleration (ac) is a measure of how an object moving in a circle is being drawn towards the center of the circle measured in m/s/s.
Conversions:
converting from angular (radians) measurements to linear (meters) measurements:
tangential velocity: v = rω (meters/sec)
tangential acceleration: a = rω2 (meters/sec2) = rα
Let's take a gander at the Homework:
HW Probs:
Conceptual Problem #6 on page 168, Problems 2, 3, 4 and 7 on page 169. Also, let's turn back to chapter 4 and do #39....
If you're up for a nasty challenge, try researching the diff eq 6.5 (what happens when we DO NOT ignore air friction) on page 163 (we will NOT cover this in class, but I'd love to see what you come up with)
