A Ferris wheel with a radius of 20 meters rotates at a constant speed of 0.1 revolutions per second. Determine the angular velocity, linear velocity, and acceleration of a passenger at the top of the wheel.
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To find the angular velocity, we need to convert the speed from revolutions per second to radians per second.
1 revolution = 2π radians, so 0.1 revolution per second = (0.1 * 2π) radians per second.
The angular velocity is therefore 0.2π radians per second.
To find the linear velocity, we can use the formula:
linear velocity = radius * angular velocity.
In this case, the radius is 20 meters and the angular velocity is 0.2π radians per second.
Therefore, the linear velocity is 20 * 0.2π = 4π meters per second.
To find the acceleration, we can use the formula:
acceleration = radius * angular velocity^2.
Again, the radius is 20 meters and the angular velocity is 0.2π radians per second.
Therefore, the acceleration is 20 * (0.2π)^2 = 0.4π^2 meters per second squared.
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