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    Convert Radians to Degrees

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    2π radians = 360 degrees = 1 cycle = 1 revolution
    T (period in time/cycle) = 1/f (frequency in cycles/time), and ω = 2πf
    For circular motion: s = rθ, where s = distance in units of length, r = radius, θ = angle in radians
    ω = angular velocity (or angular frequency) in radians/time or revolutions/time
    v = rω, where v = linear velocity in units of length/time, r = radius
    θ = ωt = angular distance in radians

    1. Convert 5π/2 radians to degrees. Put your answer in the range [0, 360).
    2. Convert -30 degrees to radians. Put your answer in the range [0,2π).

    A merry-go-round with a radius of 15 feet is rotating with an angular velocity of 2 rev/min.
    3. What is its angular velocity in radians/sec?
    4. What is the period of the merry-go-round in sec/cycle?
    5. How far in feet does a person on the rim travel in 1 sec?
    6. How many degrees does a person turn through in 1 sec?
    7. What is the frequency of the merry-go-round in cycles/sec?
    8. What is the linear velocity in feet/sec of a point on the rim of the merry-go-round?

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    Solution Summary

    The expert converts radians to degrees.