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Forces 5 Turning forces: 5.6 Gears and cog wheels - a means of transmitting a rotational force effect

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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

Thomastown, Co. Kilkenny

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.

explaining diagram of how bicycle gears work cogwheel ratios explained going up a gear to go faster gcse physics igcse

'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.

explaining diagram of how bicycle gears work cogwheel ratios explained going down a gear to go up a hill gcse physics igcse

'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

Worked out ANSWERS to the moment calculations

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?

The 2nd gear wheel must turn anticlockwise - it must turn in the opposite direction.

The 2nd gear wheel will turn 25/5 x 2 = 10 revolutions

Argument: The 25 teeth of the first gear wheel will move 25 teeth of the smaller gear wheel. Since the 2nd smaller wheel only has 5 teeth, the 25 teeth of the larger gear wheel will move it 5 times per revolution and this is doubled for two revolutions of the 1st larger wheel. The gear ratio is 5 : 1.

 

Index Forces 5. Turning forces, calculating moments, problem solving

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