Final answer:
To find the maximum linear speed of an 11.8-mm-diameter drill bit rotating at 1400 rev/min, calculate the angular velocity in radians per second and then use the formula v = r⋅ω with the radius in meters.
Step-by-step explanation:
The student has asked to find the maximum linear speed of any part of an 11.8-mm-diameter drill bit turning at a constant 1400 revolutions per minute (rev/min). When a circular object rotates, each point on the edge of the object follows a circular path. The linear speed (also known as tangential speed) of a point on the edge of a rotating object is a measure of how fast this point moves along its circular path. To calculate the linear speed (v) of any point on a rotating drill bit's edge, we need to use the relationship v = r⋅ω, where r is the radius of the drill bit, and ω is the angular velocity.
The angular velocity (ω) can be found by converting the given rotational speed from rev/min to radians per second. There are 2π radians in one revolution, and there are 60 seconds in a minute, so the conversion is done by multiplying the given speed by 2π and then dividing by 60.
By substituting the radius of the drill bit, which is half of the 11.8-mm diameter, into the formula v = r⋅υ, and using the calculated angular velocity, we can find the maximum linear speed of the point on the edge of the drill bit.