In the spin cycle of a clothes washer, the drum turns at 635 rev/min. If the lid of the washer is opened, the motor is turned off. If the drum requires 8.0 s to slow to stop, what is the angular acceleration of the drum?
(-635rev/min)/(8s) = -79.375 rev/min/s
you can convert that to rev/min^2 or rev/s^2
you didn't say what you wanted.
and then 1 rev = 2 pi radians so you can get radians/s^2 which is the most common unit of angular acceleration.
To find the angular acceleration of the drum, we can use the following formula:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time
Given:
Initial angular velocity (ω₀) = 635 rev/min
Final angular velocity (ω) = 0 rev/min (since the drum slows to stop)
Time (t) = 8.0 s
First, let's convert the initial and final angular velocities to radians per second:
ω₀ = 635 rev/min * (2π rad/rev) * (1 min/60 s) = 66.81 rad/s
ω = 0 rev/min = 0 rad/s
Now we can calculate the angular acceleration:
α = (ω - ω₀) / t
α = (0 rad/s - 66.81 rad/s) / 8.0 s
α = -66.81 rad/s / 8.0 s
α = -8.35 rad/s²
Therefore, the angular acceleration of the drum is -8.35 rad/s². Note that the negative sign indicates that the drum is decelerating.
To find the angular acceleration of the drum, we first need to find the initial angular velocity of the drum before it slows down.
We know that the drum turns at 635 rev/min. To convert this to radians per second, we need to multiply by 2π (since there are 2π radians in one revolution) and divide by 60 (since there are 60 minutes in one hour):
Angular velocity (ω) in radians per second = (635 rev/min) * (2π radians/rev) / (60 min/hour)
Now, let's calculate ω:
Angular velocity (ω) = (635 rev/min) * (2π radians/rev) / (60 min/hour)
= (635 * 2π) / 60 radians/second
Next, we need to find the final angular velocity when the drum slows down and stops. We know that the drum requires 8.0 seconds to slow to stop, so the final angular velocity (ωf) will be zero.
Now we can use the following equation to find the angular acceleration (α) of the drum:
Final angular velocity (ωf) = Initial angular velocity (ω) + (angular acceleration (α) * time (t))
Since ωf is zero, we can rearrange the equation to solve for α:
Angular acceleration (α) = -ω / t
Now let's substitute the values we have:
Angular acceleration (α) = -(angular velocity (ω)) / time (t)
= -(ω) / 8.0 s
Finally, we can substitute the value of ω we calculated earlier to find the angular acceleration of the drum.