2. On the spin cycle on a washing machine, the drum holding the clothes goes from zero to 180 rpm (revolutions per minute) in 8.0 seconds. (Hint: Be sure to change rpm to radians/sec.)

(a) What is the angular acceleration (in radians/sec2) during this time period?

(b) How many revolutions does it take for the drum to reach 180 rpm?

1 revolution=2π radians

1 minute = 60 seconds

(a)
Angular acceleration
= 180 rpm/8 s
=22.5 rpm / s
= 22.5*(2π) radians/60s /s
=3π/4 rad/s²

(b)
No. of revolutions
=average angular speed * time
=(0+180)/2 rpm * (8/60) min
= 12 revolutions

(a) To find the angular acceleration (in radians/sec^2), we need to use the formula:

angular acceleration = (final angular velocity - initial angular velocity) / time

First, we need to convert the final angular velocity from rpm to radians/sec. Since 1 revolution is equal to 2π radians, we can calculate the final angular velocity as follows:

final angular velocity = 180 rpm * (2π radians/1 revolution) * (1 minute/60 seconds) = 6π radians/second

Next, we need to convert the initial angular velocity from 0 rpm to radians/sec, which is 0 radians/second.

The time given is 8.0 seconds.

Now, we can plug in the values into the formula to find the angular acceleration:

angular acceleration = (6π radians/second - 0 radians/second) / 8.0 seconds
= (6π radians/second) / 8.0 seconds
= 3π/4 radians/second^2

Therefore, the angular acceleration during this time period is 3π/4 radians/second^2.

(b) To find how many revolutions it takes for the drum to reach 180 rpm, we can divide the final angular velocity by the angular velocity per revolution.

The angular velocity per revolution is given by:

angular velocity per revolution = 2π radians / 1 revolution

Now, we can calculate the number of revolutions:

number of revolutions = (final angular velocity) / (angular velocity per revolution)
= (6π radians/second) / (2π radians/revolution)
= 3 revolutions

Therefore, it takes 3 revolutions for the drum to reach 180 rpm.