15.1-15.4 Rotation about a Fixed Axis
Gears with Belts:
See example problems:
Gears with Belts:
Bike Gears:
See example problem:
Use
the toy bike to help conceptualize bike gears:
http://cyclingtips.com.au/2014/08/beyond-the-big-ring-understanding-gear-ratios-and-why-they-matter/
Gear ratios are
specified by the number of teeth per gear.
The rear sprocket turns the back wheel, while the chainring is connected
to the foot petals. The number of wheel
revolutions produced by a bike’s gearing is determined by the ratio of the
chainring (crank) to the rear sprocket (Cog).
Example: a 53T crank with 12T
cog, has a ratio 53:12 or 4.42 — which means the rear wheel rotates 4.42 times
for every rotation of the crank.
(1 mile = 5,280 ft = 63,360 inches)
The fastest
officially recorded bike speed was 51.28 mph by Jim Glover in 1986.
- If Jim produced this record on 53T/12T, how fast (rpm) would he have had to pedal?
- If Jim’s bike had a 12T/106T gear ratio, how fast would he have had to pedal?
Old Fashioned bike:
Explain the logic
behind the design of old-fashioned bikes.
For an old-fashoned high-wheeler bike:
If
the front wheel is 4 feet in diameter, and the person pedals at 70 rpm’s, how
fast, in mph, would they travel? How does the size of the front wheel compare to gear combination on a modern bike?
The larger the front wheel of the high-wheeler bike is, the __________ (easier or harder) it is to pedal.
How fast can a
unicycle with a 27” diameter tire pedaled at 70rpm go?
Waterwheels:
Relate the velocity
of the water to the velocity of the uppermost gear.
What gear ratios
would you choose if you wanted the uppermost gear to rotate twice as fast as
the waterwheel?
What gear ratio would you use if you needed the waterwheel to produce a large torque (rather than a large RPM)?
See example problems:
Extra Credit:
Design a set of gears for
a watch to correctly move the hour, minute, and second hands.
What other
applications are gears used for?
If you are done early, start working on chapter 15 HW!
Just for fun:
