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