# Convert Radians to Degrees

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?

https://brainmass.com/math/basic-calculus/convert-radians-degrees-613294

#### Solution Summary

The expert converts radians to degrees.