**Lecture and do-it-yourself demonstrations**

Dynamics, TAM 2030, Cornell

** 1) Drop two balls, ** a big ball and a small ball (do it yourself
= DIY, and lecture). They hit the ground at the same time. Why?

To Galileo that was a principle in itself. But in Dynamics, with* F=ma, *it's
something we have to figure out.

Use any wildly disparately-sized balls or objects for the demo.
Use *F=ma* to predict the result.

**2)** **Drop two cones** (DIY and lecture)**.** Two
paper cones are made with the same
paper and have the same conical angle. One has twice the radius as the other.
Which falls faster? Print two
copies of **this sheet** and cut
out to make the **cones** and do
the **experiment**.
Use *F=ma* to predict the result. Hint: the cutout lets you think about
how to calculate the area of the paper used to make the cone. The result holds
for linear or quadratic drag, or a combination of both. It holds for the steady
state or for the transient response.

**3) Spring and mass.** **a)** using air track (with
air pump and all in lecture. See (5) below.),** b) **using self
as imagined mass walking back and forth with imagined force pushing this way
and that (DIY & lect).** c) **Using
a spring and mass held by hand** (video). d)** DIY: Hang a shoe
with a rubberband.

**4) Forced oscillations and damping.** **1)** Use **apparatus** from
old TAM 203 lab. Can be used with no data collection. **2)** Use
spring and mass, or rubberband and shoe, and vertically oscillate your support
hand. Note fast hand motions leads to fast small 180-degree-out-of-phase motions. Slow
hand motions leads to mass moving up and down with hand. Resonant hand motions
lead to large oscillations

.

**5)** **Two DOF oscillations**. Use the **air
track** used for Spring and mass above (from old TAM 203 lab). Shows
normal modes and, if you pick the motor speeds correctly, resonance of either
mode.

**6)** **Normal modes of a slinky **(video).

**7) Normal modes of a dulcimer** (video). Excite
various modes by putting one finger lightly on a node when plucking. Change
relative intensity of modes, changing "tone" by plucking with fingernail near
the end.

**8) Collisions using airtrack.** Using airtrack from (5) above.
Take off springs and then bounce masses together *(e~1*). And again
with chewing gum in between (approximately *e~0*).

**9)** **Trajectories (3 demos): a)** Throw chalk,
eraser or ball and note parabolic trajectory; **b)** Throw wad
of paper and note trajectory is not parabolic, but falls more vertically at
the end; **c)** Use
spray bottle almost tangent to blackboard, and aimed up to show trajectories
of droplets
of water left as streaks on the blackboard, draw on top with chalk to show
a variety of trajectories.

**10)** **Colliding balls in space. **Throw two
balls in air and
watch them collide: throw, fly, bang, try to catch. The demo is unrealistic
because the balls have finite friction and the simple calculation for spatial
collisions assumes no friction.

**10) Human demo of pulleys****. **Use students
or prof. as mass, force or wall. Pulley either goes with force or mass. In
the photo the left student is a mass holding a pulley (string sliding through
fingers), the middle student is a solid wall, and the right student applies
a force. Therefor the left student has acceleration *2F/m* and the right student
has acceleration *4F/m*.

**11) Simpler version of above.** Two students connected by a
rope. Prof pulls on one of them. Showing the idea that if there are kinematic
constraints one has to either **a)** finesse finding the constraints,
e.g., by using system linear momentum balance, or **b)** Use kinematics
equations as supplementary equations to help solve for constraint forces.

**12) Simple pendulum.** Hang a mass from a string (e.g., a pocket
knife). Note various things: circular motion, effect of string tension, simultaneous
validity of polar coordinate and cartesian representations.

**13) Rotated drawing.** Draw on cardboard. Pin one point by
pressing with finger. Rotate the drawing about the finger-hinge. Show how body
fixed coordinates do
not change in time but space-fixed coordinates do.

**14)** **Physical pendulum** (a yard stick suspended
from a nail).

**15) ** **A clipboard suspended by a spring.** Used as example for setting up 2D
equations of motion of a rigid object in space

**16)** **Movie spool.** Showing various effects: pulling gently straight off bottom,
pulling up, pulling at an angle, pulling hard

**17)** **Kinematics of rolling** using a disk rolling against the
blackboard (using a 1960s hard-drive disk, but any disk will do). Draw the cycloid.

**18)** **A disk rolling down hill.** And down** a
steep hill** so it
slides instead of rolls.

**19)** **A disk on a table cloth** with the cloth
pulled out from underneath (surprising answer: final rolling is at zero velocity).

**20)** **A cube is balanced on one edge then falls** onto another edge/corner and then tips up a bit.

**21) Video of collisions in a walking robot.**

**22) "New gun"**. Nut slides on rotating rod and shoots
dangerously accros the room. Good illustration of use of polar coordinates.

**23)** **Slider crank:** lawn-mower engine and
hand-crank model.

**24) Photo finish of bicycle race: **explain the spoke patterns.
Compare top photos with lower photo (that Andy took):

Here is
a video of a TAM student Derek Faust's Matlab simulation of the effect.

**25) **Compare the period of oscillations of a **swinging
hoop** with diameter D
and a simple pendulum with length D. They match.

**26) Spool sliding down a slope.** The funny thing is that the
bottom of the spool slides UP the slope.

**27) Comparing and arrow with feather with an arrow with a ball at
the end**,
using chopsticks.

**28) Pull on the bottom of a bicycle pedal, backwards.** Which
way does the bicycle go? What if you pull hard?

**29) Stick balancing using hand and stick**. Using sideways
acceleration, using wrist torque (with feedback) , using stiff wrist (open
loop).

**30) Balance by vertical oscillation of support.** Scotch-yoke
demo. Also video of same.

**31) Video of human balance with 10:1 exaggrated horizontal motion.** Also,
people standing and thinking about their own ankle feedback loops.

**32) Double ** **Double-pendulum.** Shown as a
single pendulum, compared with another to show matching of solutions. As a
double pendulum, showing chaos (Demo made by Jason Cortell to Steve Strogats'
specs.