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Stonehenge

Age 16 to 18
Challenge Level Yellow star
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Here's a good clear explanation from Jack of Madras College.

Consider the movement of the block relative to the logs:

When the log makes one revolution it travels ${\pi}d$ metres. As the block is in contact with the logs, it moves ${\pi}d$ metres along the horizontal plane.


Therefore, the block moves ${\pi}d$ metres relative to the logs.

Now consider the movement of the logs relative to the ground:

When the log makes one revolution it rotates ${\pi}d$ metres. As it is in contact with the ground it moves ${\pi}d$ metres along the horizontal plane.

Therefore, the log moves ${\pi}d$ metres relative to the ground.

This means the log moves ${\pi}d$ metres relative to the ground but the block moves ${\pi}d$ metres relative to the logs.

Therefore, the block moves $2{\pi}d$ metres relative to the ground, which is twice as much as the logs.

Thus:- the block moves twice as fast as the logs .

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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