A es004-1.jpginch circular saw blade rotates at 5200 revolutions per minute.
a) Find the angular speed of the saw blade in radians per minute.
b) Find the linear speed in feet per minute of one of the 24 cutting teeth as they contact the wood being cut.
a) angular velocity = 5200(2π) radians/ minute
= appr 3267 radians/min
b) can't make out the radius of the saw blade.
Anyway, do it the same way I just showed you in your previous post
a) To find the angular speed of the saw blade in radians per minute, we need to convert the given value of revolutions per minute (rpm) to radians per minute (rad/min).
We know that one revolution is equal to 2π radians, so to convert from rpm to rad/min, we can use the following conversion factor:
1 rpm = 2π rad/min
The given saw blade rotates at 5200 revolutions per minute, so the angular speed in radians per minute can be calculated as:
Angular speed = (5200 rpm) * (2π rad/min)
Angular speed = 10400π rad/min
Therefore, the angular speed of the saw blade is 10400π radians per minute.
b) To find the linear speed in feet per minute of one of the cutting teeth as they contact the wood being cut, we need to know the diameter of the circular saw blade.
Since the diameter of the saw blade is not given in the question, let's assume it is D inches.
We know that the circumference of a circle is given by the formula:
Circumference = π * Diameter
So the length of one complete rotation of the saw blade is equal to the circumference of the circle formed by the blade.
Given that the circular saw blade has 24 cutting teeth, the length covered by one tooth as it contacts the wood during one rotation is equal to the circumference divided by 24.
Length covered by one tooth = (Circumference of blade) / (Number of teeth)
Length covered by one tooth = (π * D) / 24 inches
Now, to convert the length from inches to feet, we can divide by 12, since there are 12 inches in a foot.
Length covered by one tooth = ((π * D) / 24 inches) / 12
Therefore, the linear speed in feet per minute of one of the 24 cutting teeth as they contact the wood being cut is ((π * D) / 24) / 12 feet per minute.