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Chap 15 lab

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.


The optimal pedal rate for typical bikers is 60-90 revolutions per minute.  Determine the speed in miles per hour of a biker pedaling at 70 rpm whose tires have a diameter of 27 inches, with cranks: 53T, 50T, 47T, and cogs: 12T, 15T, 20T.   
(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: