London Eye

London Eye - the giant rotating wheel with 32 capsules makes for a good physics study as it involves all sorts of questions in mechanics. The capsules have a mass of 10,000 kg and are 68 m from the centre. When moving they travel at a constant speed of 0.26 m/s. Consequently the centripetal force can be calculated from F = mv*2/r - (10,000)(.26)*2/68 = 9.9 N. ( not very different from earths gravitational force).
The angular speed in rad/s can be shown from v=rw as .0038 and the time for one complete rotation ( 2 pi r ) is about 27 minutes.
When it starts up it needs an average net torque of 46 million newton metres to accelerate it up to speed - i.e. an average angular acceleration of .0017 rad/s/s
In that start up time it rotates through 1/4 of a degree.
As the wheel increases its speed the frictional forces acting against the motion increases causing the unbalanced torque and the angular acceleration to decrease. When the torques reach balance there will be no further acceleration and the wheel now travels at constant speed. So there is no change in kinetic energy and the motor is simply matching the friction.
When a capsule is at the top it can sway a maximum of 0.15 m ie in SHm of 1.8 rad/s
If I was sitting in a capsule with this amount of sway would be moving sideways at about 2.6 m/ the start of the swing. Dampers are used to restrict the sway - otherwise the sway could be as much as 3 m in a strong wind.

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