An automatic dryer spins wet clothes at an angular speed of 4.4 rad/s. Starting from rest, the dryer reaches its operating speed with an average angular acceleration of 4.2 rad/s2. How long does it take the dryer to come up to speed?
V = Vo + at = 4.4 rad/s.
0 + 4.2t = 4.4
t = 4.4/4.2 = 1.05 s.
To find the time it takes for the dryer to come up to speed, we can use the formula:
ω = ω0 + αt
where:
ω = final angular speed (4.4 rad/s)
ω0 = initial angular speed (0 rad/s, since it starts from rest)
α = angular acceleration (4.2 rad/s²)
t = time
Rearranging the formula to solve for time (t):
t = (ω - ω0) / α
Substituting the given values:
t = (4.4 rad/s - 0 rad/s) / 4.2 rad/s²
t = 1.048 seconds
Therefore, it takes the dryer approximately 1.048 seconds to come up to speed.
To find the time it takes for the dryer to come up to speed, we can use the formula:
ω = ω0 + αt
Where:
ω is the final angular speed (4.4 rad/s),
ω0 is the initial angular speed (0 rad/s since it starts from rest),
α is the average angular acceleration (4.2 rad/s²),
and t is the time we want to find.
We rearrange the formula to solve for t:
t = (ω - ω0) / α
Substituting the given values:
t = (4.4 rad/s - 0 rad/s) / 4.2 rad/s²
Calculating this equation:
t = 1.048 s
Therefore, it takes approximately 1.048 seconds for the dryer to come up to speed.