Angular speed is the rate at which an object changes its angle (measured) in radians, in a given time period. Angular speed has a magnitude (a value) only.
Angular speed = (final angle) – (initial angle) / time = change in position/time
ω = θ /t
ω = angular speed in radians/sec
θ = angle in radians (2π radians = 360 degrees)
t = time, sec
Angular speed and angular velocity use the same formula; the difference between the two is that Angular speed is a scalar quantity, while angular velocity is a vector quantity.
Angular Speed Formula Questions:
1) The earth rotates once on its axis every 24 hours. What is its angular speed?
Answer: The angle traversed, 1 rotation, means that θ = 2π. The time for this rotation, t = 24 hr. Time must be converted to seconds.
t = 24 hr x 60 min/hr x 60 sec/min = 86400 sec
ω = θ /t
ω = 2π/86400 sec
ω = 0.0000726 radians/sec = 7.26 x 10-5 rad/sec
2) At the state fair, you take your younger brother to ride the Ferris wheel. You notice that a sign says that the angular speed of the Ferris wheel is 0.13 rad/sec. How many revolutions will the wheel complete in 12 minutes?
Answer: The angular speed, ω = 0.13 rad/sec. The time, t = 12 min. Convert t = 12 min x 60 sec/min = 720 sec. Using the equation ω = θ /t , solve for θ .