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Forces 5 Turning forces: 5.6
Gears and cog wheels - a means of transmitting a rotational force effect
Doc Brown's Physics exam study revision notes
Index of physics notes: 5.
Turning forces, calculating moments, problem solving
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5.6 Gears and cog
wheels - a means of transmitting a rotational force effect
Some simple calculations are included at the
end of section (f)
Cog wheels
are circular discs with teeth and components of many machines in transport and
industry.
They are a means of transmitting the rotational effect of
a force from one part to another part of a mechanical device e.g. industrial
machine, motor vehicle or a bicycle.
When several of them are
combined together (linked in contact via the teeth) a rotational force can be transmitted when fitted in contact
with each other. The cog/gear wheels when in direct contact will rotate in
opposite directions.
Through the interlocking, one cog wheel can turn another in the
opposite direction i.e. if one gear wheel goes clockwise, the gear
wheel in contact with it will go anticlockwise, no matter how many gear
wheels are connected together.
By using different size cog wheels differing in the number
of teeth, you can increase or decrease the force generated by the turning effect
of the gear wheels.
From the gear ratio you can work the
revolutions of one gear wheel with respect to the neighbour wheel e.g.
in the diagram gear wheel 1 has 12
teeth and gear wheel 2 has 18 teeth.
If the smaller wheel 1
turns once, wheel 2 turns 2/3 third of a revolution, teeth ratio
12/18 = 2/3 (0.66).
It the larger wheel 2 turns once,
wheel 1 turns 1.5 revolutions, teeth ratio 18/12 = 3/2 = 1.5.
The teeth ratio gives you the
gear ratio.
A force applied to a smaller gear wheel
creates a small moment
- shorter distance from the teeth to the axle pivot
point.
A force applied to a larger gear wheel
creates a larger moment
- longer distance from the teeth to the axle pivot
point.
As moment = force x distance,
the
ratio of the two moments of the ears is equal to the ratio of the gear radii
which equals the ratio of the teeth.
If you transfer the force from a larger cog wheel (gear wheel
of more teeth) to a smaller cog wheel (gear wheel of less teeth) you decrease
the moment of the 2nd as you have decreased the distance from the
applied force to axle pivot point.
No mechanical advantage is gained
- you haven't increased the output force of the smaller cogwheel.
The smaller cog wheel will be made to
turn faster than the larger cog wheel.
This is a way to increase rotational
speeds in machines.
If the first cog wheel has 20 teeth and
the second cog wheel 5 teeth, one rotation of the first wheel causes the
smaller wheel to rotate 20/5 times = 4 x more - a gear ratio of 1 : 4.
If it was the other way round and you
rotated the 2nd smaller cog wheel first, one turn of it would only
rotate the larger cog wheel by 1/4 (5/20) of a turn - a gear ratio of 4
: 1, decreasing the speed of rotation.
If you transfer the force from a smaller cog wheel (gear
wheel of less teeth) to a larger cog wheel (gear wheel of more teeth) you
increase the moment as you have increased the distance from the applied
force to the axle pivot point.
A mechanical advantage is gained
-
you have increased the output force of the larger cogwheel.
By using a set of interlocking gears that
get bigger and bigger you can multiply the moment of the first small gear.
The larger cog wheel will turn more
slowly than the smaller one.
This is the way a relatively low powered
machine can be made to lift heavy weights.
If the first cog wheel has 8 teeth and
the second wheel 56 teeth, you need to turn the first wheel 56/8 = 7 times
to completely rotate the second wheel.
Examples of gear wheel (cogwheel)
applications
An old fashioned manual drill
The large cog wheel turns a smaller cog wheel at much greater
speed with good old fashioned muscle power!
The force is transmitted from one cog wheel to another.
Since a larger cog wheel of more teeth drives a smaller cog
wheel of less teeth, the output is a high turning speed of the drill.
Gearing in mill wheel systems
Complex machines such as you find in older flour mills and
textile mills, use
gears to utilise the power of the e.g. water wheel, to transmit a force to drive the
machinery with the required speed and power.
A slow rotating water wheel driving a cog wheel system ( a
gear system)
can produce high speeds of rotation to drive a spinning machine - an important
mechanical feature in the Industrial Revolution from the 18th to the 19th
century.
Clocks
Clocks use gear wheels to transmit
the potential energy of the spring and move the arms around at the
correct speed to indicate the correct time.
Different sized gear wheels
are need to operate the minute and hour hands.
The minute hand must go
round 60 x faster than the hour hand, so the gear ratios will take this
into account.
Gears on bicycles
Gears (cogwheels) are used in
bicycles to transfer the force from pedalling the front gears to the
gears on the rear wheels.
The gears are not in contact with
each other, but the cogs are connected by a continuous chain mechanism.
The force of your foot applied to the
pedal rotates the first gear (front cog) and, via the chain, the rear
gear (rear cog) is rotated in the same clockwise direction.
If the cogs are the same size (same
number of teeth), they both rotate at the same speed.
Bicycles often have complex sets of gears
for efficiently transferring the force generated by pedal action to driving
the rear wheel.
The following
two 'simplified' diagrams and notes explain the 'physics' principles behind
gear changes on a bicycle.
'Speeding up' - especially
downhill !!!
Apart from greater physical
exertion, in order to speed up when cycling, you change to a higher
gear.
You do this by switching to a
smaller rear gear wheel on the back wheel, the smaller gear wheel
rotates faster, but with a smaller force e.g.
The front gear has 12 teeth (or
cogs) and the rear cogwheel 8 in the diagram above.
The ratio is 12/8 = 1.5, so every
time you pedal the front cog round once, the rear cog and wheel are
turned 1.5 times - this assumes the gear teeth of both
cogwheels are the same size so the radius ratio of the cogwheels is
3 : 2.
The gear ratio change can be as high as a
53 to 11 ratio to go fast, so one pedal cycle rotates the rear wheel nearly
five times, but this gear ratio can be hard work!
With a triple chainring on the
front gear and 10 gear set on the rear wheel, you have a choice of
30 gear ratios for fastest speeds on the flat or downhill or
climbing the steepest hills.
'Tackling a steep hill'
Apart from greater physical
exertion, in order to climb up a steep hill when cycling, you change
to a lower gear.
You do this by switching to a
larger rear gear wheel on the back wheel, the larger gear wheel
rotates more slowly, but with a larger force e.g.
The front gear has 8 teeth (or
cogs) and the rear cogwheel 12 (ratio 2/3) in the diagram above, so
one turn of the front gear by the pedals only produces 2/3rds of
turn of the rear cog and rear wheel.
If the ratio the front cog : rear
cog was 1 : 3, the mechanical advantage is 3 - this assumes the gear
teeth of both cogwheels are the same size so the radius ratio of the
cogwheels is 1 : 3.
This means the input force
produces an output force 3 x greater, but you do a lot of
pedalling to generate a continuous output of a force sufficient
to get up a steep hill.
Gear wheel questions
Q1 A 25 toothed gear wheel is in
contact with a 2nd gear wheel with 5 teeth.
When the first wheel is turned
twice clockwise, in what direction does the 2nd wheel turn and by
how many times?
Worked out ANSWERS
Index of Forces 5.
Turning forces, calculating moments, problem solving
Keywords, phrases and learning objectives for turning forces
How gears cog wheels ratios transmit a rotational
turning force calculations based on cog wheel ratios bicycle gears
bikes mill wheels clocks
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Index of Forces 5.
Turning forces, calculating moments, problem solving
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