Question

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.250 rev/s . The magnitude of the angular acceleration is 0.896 rev/s2 . Both the the angular velocity and angular accleration are directed counterclockwise. The electric ceiling fan blades form a circle of diameter 0.760 m. Compute the fan's angular velocity magnitude after time 0.207 s has passed.

Answer 1

ω = 0.436 rev/sec = 2.736 rad/sec

Step-by-step explanation:

By definition, the angular acceleration is the rate of change of angular velocity, which is described by the following expression:

`\alpha = (wf-wo)/(t-to)`

Solving for ωf :

ωf = ω₀ + α*t (assuming t₀ = 0)

Replacing by givens in the problem, ω₀ = 0.250 rev/s, t =0.207 sec, and α = 0.896 rev/s², we have:

ωf = 0.250 rev/s +( (0.896 rev/s²)*(0.207 s)) = 0.436 rev/sec

Expressed in rad/sec:

ωf
`= 0.436 rev/sec*2*\pi =2.736 rad/sec`