Honors Pre-Calc.. Dealing with angular speed

Question

The drum in a washing machine spins at 1200 revolutions per minute. if the diameter of the drum is 76 centimeters, find the angular speed of the drum in radians per second.

Can whoever solves this tell me how they got time in the formula for angular speed: w=θ/t

Answer 1

Each revolution is 2π radians, so you just multiply by 2π radians/revolution to get

1200 revolutions/min × 2π radians/revolution = 2400π radians/min for the angular speed.

Since you need your answer in radians/sec you multiply again by (1 min) / (60 sec) to get

2400π radians/min × (1 min) / (60 sec) = 2400π/60 radians/sec = 40π radians/sec

Answer

ω = 40π radians/sec ≈ 125.7 radians/sec [where ω is the commonly used symbol for angular speed]

Answer 2

One revolution is one full turn around a circle, so the angular measure of one revolution is 2π radians.

So 1200 revolutions is 1200(2π) = 2400π radians.

Since the speed is 1200 revolutions per minute, that's 2400π radians per minute.

We want the speed in radians per second, though.

Since one second is 1/60 of a minute, we need to multiply by 1/60:

2400π x (1/60) = 40π radians per second.

Notice that we didn't need to know the diameter of the drum for this problem.

We could also solve this problem with a "units analysis" approach:

1200 rev 2π rad 1 min 40π rev

-------------- x ----------- x ------------- = --------------

min rev 60 sec sec