A high-speed sander has a disk 8.00 cm in radius that rotates about its axis at a constant rate of 1100 revolutions per minute. Determine the angular speed of the disk in radians per second.
Just convert 1100 rpm to radians per second. The radius has nothing to do with the answer.
100 rev/min * (1 min/60 s)*(2 pi rad/rev) = ___ rad/s
115.19
To determine the angular speed of the disk in radians per second, we need to convert the given speed from revolutions per minute (rpm) to radians per second.
1 revolution = 2π radians
To convert from rpm to radians per second, we'll use the following conversion factor:
1 minute = 60 seconds
First, let's find the angular speed in radians per minute:
Angular speed in radians per minute = (1100 rpm) * (2π radians/1 revolution)
= 2200π radians/minute
Next, we'll convert the angular speed from minutes to seconds by multiplying it by the conversion factor of 1 minute = 60 seconds:
Angular speed in radians per second = (2200π radians/minute) * (1 minute/60 seconds)
= (2200π/60) radians/second
Simplifying further:
Angular speed in radians per second ≈ 36.389 radians/second
Therefore, the angular speed of the disk is approximately 36.389 radians per second.
To determine the angular speed of the disk in radians per second, we can use the following formula:
Angular speed = (angular velocity in revolutions per minute) * (2π radians/1 revolution) * (1 minute/60 seconds)
Given that the angular velocity is 1100 revolutions per minute, we can substitute this value into the formula:
Angular speed = 1100 revolutions per minute * (2π radians/1 revolution) * (1 minute/60 seconds)
Now, let's simplify the equation:
Angular speed = 1100 * 2π / 60 radians per second
Angular speed = 1100 * π / 30 radians per second
Angular speed ≈ 114.6 radians per second
Thus, the angular speed of the disk is approximately 114.6 radians per second.