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If a wheel makes 12 of a rotation in 2 seconds, what is the angular velocity, in radians per second?

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Answer:

angular velocity = 12π Radians per second

Step-by-step explanation:

The angular velocity is a measure of the rotation/revolution speed of an object, relative to another point.

In order to present the answer in radians per second, let us first establish the relationship between radians and rotations/revolution.

one complete revolution = 360° = 2π Radians

∴ 1 roration = 2π Radians

12 rotations = 12 × 2π Radians = 24π Radians

Angular velocity in radians = 24π Radians in 2 seconds

Now let us convert to radians per seconds.

24π Radians = 2 seconds

2 seconds = 24π Radians

∴ 1 second = (24π Radians) ÷ 2

1 second = 12π Radians

∴ angular velocity = 12π Radians per second

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