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A hamster running in a wheel of radius 10 cm spins the wheel one revolution in 9 seconds. What is the angular velocity of the wheel?

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Final answer:

The angular velocity of a hamster's wheel with a radius of 10 cm that completes one revolution in 9 seconds is approximately 0.698 radians per second.

Step-by-step explanation:

The student asked about the angular velocity of a hamster's wheel. Angular velocity is defined as the rate of change of angular displacement and is usually represented by the symbol ω (omega). Given that the wheel has a radius of 10 cm and completes one revolution in 9 seconds, we can calculate the angular velocity. One complete revolution means the wheel turns through an angle of 2π radians. Therefore, the angular velocity ω is equal to 2π radians divided by the time for one revolution, which is 9 seconds.

Using the formula:

ω = Θ / t

Where ω is the angular velocity, Θ is the angle in radians (which is 2π for one complete revolution), and t is the time in seconds. We can compute the angular velocity:

ω = 2π / 9

Therefore, the angular velocity of the wheel is approximately 0.698 radians per second.

User Ryan Arief
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