Angular Velocity Calculator:
Enter the values of change in angle α2(rad) – α1(rad) and time taken, t(s) to determine the value of angular velocity, ω(rad/s).
Angular Velocity Formula:
Angular velocity, often denoted by ω (omega), is defined as the rate of change of angular displacement and is a measure of how fast an object rotates or revolves relative to another point.
Angular velocity, ω(rad/s) in radians per second is calculated by dividing the change in angle α2(rad) – α1(rad) in radians by the time taken, t(s) in seconds.
Angular velocity, ω(rad/s) = α2(rad) – α1(rad) / t(s)
ω(rad/s) = angular velocity in radians per seconds, rad/s.
α2(rad) – α1(rad) = change in angular positions in radians, rad.
t(s) = time in seconds, s.
Angular Velocity Calculation:
1.A fan rotates from an angular position of 0 radians to an angular position of 10 radians in 5 seconds. Calculate the angular velocity.
Given: α2(rad) – α1(rad) = 10 – 0 = 10rad, t(s) = 5s.
Angular velocity, ω(rad/s) = α2(rad) – α1(rad) / t(s)
ω(rad/s) = 10 / 5
ω(rad/s) = 2rad/s.
2.A wheel rotates through an angular displacement of 30 radians at a constant angular velocity of 15 radians per second. Calculate the time taken for this rotation.
Given: α2(rad) – α1(rad) = 30rad, ω(rad/s) = 15rad/s.
Angular velocity, ω(rad/s) = α2(rad) – α1(rad) / t(s)
t(s) = α2(rad) – α1(rad) / ω(rad/s)
t(s) = 30 / 15
t(s) = 2s.