The wheel of a bicycle is rotating from rest at a constant rate of 5.11rad/s2. How much is the increase in angular velocity (in rpm) every minute?
To find the increase in angular velocity in revolutions per minute (rpm) every minute, we need to convert the given angular acceleration from radians per second squared (rad/s^2) to revolutions per minute per minute (rpm/min^2).
Here's the step-by-step process:
1. First, we need to convert the angular acceleration from rad/s^2 to revolutions per minute per second (rpm/s).
To do this, we know that:
1 revolution = 2π radians (or 1 radian = 1/(2π) revolutions)
1 minute = 60 seconds
So, to convert rad/s^2 to rpm/s, we'll multiply the given angular acceleration by (1/(2π)), since 2π radians is equal to 1 revolution.
5.11 rad/s^2 * (1/(2π)) revolutions/radian = 5.11/(2π) revolutions per second (rpm/s)
2. Next, we need to convert the angular acceleration from rpm/s to rpm/min.
Since there are 60 seconds in a minute, we can multiply the value obtained in step 1 by 60 to convert rpm/s to rpm/min.
5.11/(2π) revolutions per second * 60 seconds = (5.11 * 60)/(2π) revolutions per minute (rpm/min)
3. Finally, we can simplify the expression obtained in step 2.
5.11 * 60 = 306.6
(306.6)/(2π) ≈ 48.9
Therefore, the increase in angular velocity of the bicycle wheel is approximately 48.9 rpm every minute.