a radial arm saw has a circular cutting blade with a diameter of 10 inches. it spins at 200 rpm. what is the linear speed of one of the 12 cutting teeth on a blade?
distance covered in 1 rotation = 10π inches
distance covered in 200 rotations = 2000π inches
speed = 2000π inches per 1 minute
you did not specify which units your answer should be in.
To find the linear speed of one of the cutting teeth on a circular blade, we need to calculate the circumference of the circle covered by the cutting teeth in one revolution.
The circumference of a circle is given by the formula: C = πd, where C is the circumference and d is the diameter.
In this case, the diameter of the circular blade is 10 inches. Therefore, the circumference is:
C = π × 10 inches
Next, we need to convert the revolutions per minute (rpm) to seconds. This can be done by dividing the rpm by 60, as there are 60 seconds in a minute. So, the revolution time in seconds is:
Revolution time = 1 minute / 60 = 1/60 minutes = 1/60 × 60 seconds = 1 second.
Now, to find the linear speed of one cutting tooth, we divide the circumference of the blade (C) by the revolution time (1 second):
Linear speed of one cutting tooth = C / Revolution time.
Substituting the values into the equation:
Linear speed of one cutting tooth = (π × 10 inches) / (1 second)
So, the linear speed of one of the 12 cutting teeth on the blade is approximately (π × 10 inches) per second.