An automatic dryer spins wet clothes at an angular speed of 4.1 rads/s. Starting from rest, the dyer reaches its operating speed with an everage angular acceleration of 4.2 rad/s^2. How long does it take the dryer to come up to speed?
We can use the following kinematic equation to solve this problem:
ω = ω0 + αt
where:
ω = final angular speed = 4.1 rad/s
ω0 = initial angular speed = 0 rad/s (starting from rest)
α = angular acceleration = 4.2 rad/s^2
t = time
Rearranging the equation, we have:
t = (ω - ω0) / α
Substituting the given values:
t = (4.1 rad/s - 0 rad/s) / 4.2 rad/s^2
t = 0.9762 s
Therefore, it takes the dryer approximately 0.9762 seconds to come up to speed.