Angular Speed Formula
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 .
ω = θ /t
ω t = θ
(0.13 rad/sec)(720sec) = θ
θ = 93.6 rad
θ = 93.6/ 2π revolutions
θ = 14.9 or ~15 revolutions
Linear Speed Formula (Rotating Object)
Tangential Velocity Formula
Distance Speed Time Formula
Angular Momentum Formula(Moment of Inertia and Angular Velocity)
Speed vs. Velocity
Torque Formula (Moment of Inertia and Angular Acceleration)
Angular Velocity Formula