At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s?

Sure, here's how you can calculate the angular speed in rad/s from rpm:

Step 1: Understand the conversion factors. We know that 1 minute has 60 seconds and 1 full rotation (revolution) is 2π radians.

Step 2: Convert the given speed from revolutions per minute (rpm) to revolutions per second. To do this, divide the given speed by the number of seconds in a minute.

So, 210 rpm = 210 revolutions/60 seconds = 3.5 revolutions per second.

Step 3: Convert revolutions per second to radians per second. To do this, multiply the result from step 2 by 2π (since 1 revolution is 2π radians).

So, 3.5 revolutions per second * 2π radians/revolution = 7π radians per second.

Therefore, the angular speed of the compact disc is 7π rad/s.