A turbine blade sweeps 6 radians in 2.0 s, turning steadily.
What is its angular velocity?
The sweep shares out evenly over the time: each second gets 6 / 2.0 = 3 radians.
So the blade's angular velocity is ω = 3 rad/s: it sweeps out 3 radians each second.
One equation says that division for every rotation.
In symbols: ω = Δθ/Δt.
You have seen this shape before: a = Δv/Δt divides a change by the time it takes. ω = Δθ/Δt is the same grammar, with the swept angle as the change.
ω comes out in rad/s when Δθ is in radians, and in °/s when Δθ is in degrees; Δt is in seconds either way.
A rotor sweeps 10 radians in 4.0 s, turning steadily. Enter its angular velocity in rad/s.
Coral says: 'A wheel with an angular velocity of 5 rad/s sweeps out 5 radians each second.' Is Coral correct?
A carousel sweeps 450° in 5.0 s, turning steadily. Calculate its angular velocity.
Write down the values:
Δθ = 450°, Δt = 5.0 s, ω = ?
Write down the equation:
ω = Δθ/Δt
Substitute in the values, and calculate:
ω = 450 / 5.0 = 90
The carousel's angular velocity is 90°/s.
A mixer blade's angular velocity is 7 rad/s. State what that means.
ω is the angle swept each second.
The blade sweeps out 7 radians each second.
A fairground ride sweeps 270° in 6.0 s, turning steadily. Enter its angular velocity in °/s.
Two merry-go-rounds turn steadily for the same time. The first sweeps twice the angle the second sweeps. How do their angular velocities compare?
An exercise bike's wheel turns at an angular velocity of 12 rad/s. Which statement is correct?
Which equation gives the angular velocity?