A centrifuge in a medical laboratory rotates at an angular speed of 3300 rev/ min. When switched off, it rotates through 59.0 revolutions before coming to rest. (a) Find the angular speed in rad/s.

To find the angular speed in rad/s, we first need to convert the units from revolutions per minute (rev/min) to radians per second (rad/s).

1 revolution is equal to 2π radians. Therefore, to convert from revolutions to radians, we need to multiply by 2π.

Given:
Angular speed = 3300 rev/min

We can convert this to rad/s using the following steps:
Step 1: Convert revolutions/min to revolutions/second
To do this, we need to divide by 60 because there are 60 seconds in a minute.
3300 rev/min ÷ 60 = 55 rev/s

Step 2: Convert revolutions/second to radians/second
To do this, we need to multiply by 2π because 1 revolution is equal to 2π radians.
55 rev/s × 2π rad/rev ≈ 110π rad/s

Therefore, the angular speed in rad/s is approximately 110π rad/s.