Microwave ovens rotate at a rate of about 6 rev/min. what is this in revolutions per second? what is the angular velocity in radians per second

With some careful thinking you can see how to get the answer right away!

there are 60 seconds in a minute, so divide the 6rev/min by 60 to get rev/sec.

Then the second bit requires you to already know what a 'radian' is. This is kind of neat but definitely something you won't "just know".

Radians are an idea, rather than an actual thing. They can be described as this: 1 radian = the length of the radius wrapped around the circumference (the outline) of the circle. The radius of a circle goes around the circumference exactly 2π times. pi = 3.14, so 2π = 6.28, which is where π actually comes from! neat imo.

So this means that in 1 minute the microwave rotates through 6 x 2π radians. So now we have the total number of radians, simply divide "6 x 2π" by 60 like we did last time to get radians per second.

The equation looks like this:

(6 x (2 x 3.14)) / 60

or

(6 x 6.28) / 60

or

37.68 / 60

= 0.628 Radians/sec