Bicycles, Rockets, Planets

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Bicycles, Rockets, Planets
Ride the bike with no hands Stability Rockets O
rbits of planets
From Goldeneye
Breaking Away
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Static Stability tricycle

• When you tilt it,
• does the Center of Gravity go up
• or down?
• Up means more PE, so falls back
• Down means less PE, so falls over

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Static stability bicycle (oops!)

• But a two-wheeler will fall over unless it is
  moving
• it is unstable!
• (thats why they have kick-stands)
• So how does it stay upright?
• Partly conservation of
• angular momentum
• stored in rotating wheels

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Faster on the curves

• Trike will tip over easily on curves
• Two wheelers lean into the turn
• to cancel centrifugal force
• Airplanes bank to make turns for the same reasons

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Why is the bike shaped like a bike?

• For instance modern bikes look like this,

Which is better? Why the change?
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Dynamic stability
r

• Bicycle tends to keep CoG
• over the the bike
• by steering into the turn
• Works whether you are riding it or not!
• Lean left then torque t r ? F
• on steering fork turns the wheel left.
• Lean right then torque t - r ? F
• on steering fork turns the wheel right.
• The more you lean the larger the torque.

F
t
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And another thing

• Wheel trails the steering axis and
• follows the bikes trajectory, but
• Its top heavy and tends to fall towards turn
  direction when you lean

Too much offset reverses the trail and makes
the bike unstable even on a straight path
(Like grocery cart casters)
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Rolling resistance and tire pressure

• As a wheel rolls, its surface dents inward
• Denting a surface requires work
• An under-inflated tire
• has a low coefficient of restitution
• doesnt return work done on it efficiently
• wastes energy (leg power) as it rolls
• This applies to car tires, too

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Bicycle gears and freewheels

• Gear ratios as before
• Free-wheels turn freely (get it?) when spun
• counter-clockwise.
• But the ratchets and pawls lock
• when you turn it clockwise.

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Braking instead of breaking

• Cantilever Brakes
• exert normal force onto wheel rims
• (another set of levers)

Caliper Brakes work like pliers
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Rocket propulsion steering

• Stuff expelled from nozzle
• Propels rocket forward or sideways
• Autonomous so momentum conserved

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Scotty to Kirk The orbit is decaying, sir

• Actually once you clear the atmosphere (and
  friction)

The only force is gravity FGRAVITY mg
Pulls toward earths center torque 0 so
cannot slow down or decay the orbit You are
actually in free-fall with some angular momentum
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Keplers orbits

• Planets (and comets, asteroids, etc) have been
  circling the sun for about 5,000,000,000 years.
• They will go on circling until the sun explodes
  or collides with another star.
• The orbits are elliptical (but pretty close to
  circular)
• and they are stable
• The year is longer for planets farther from the
  sun (T2 r3)
• so Christmas is more frequent on Mercury
• but the ski season is really just too short

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Can you jump into orbit?

• From earth ? No, because you cant jump at
  escape velocity.

Or v2 2GM/r which gives v 11,000 m/s so
thats not happening. What about jumping off of
an asteroid 1km in diameter? M gets bigger with
volume or r3 so v2 would be smaller by the
square the ratio of the earths radius to 1km So
v would be about 6000 times smaller and you might
do it if you can hold your breath long enough
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Take home messages

• Static stability
• Dynamic Stability
• Rocket propulsion and momentum conservation
• Planet orbits and free-fall