According to the shop manual, when drilling a 11.8mm--diameter hole in wood, plastic, or aluminum, a drill should have a speed of 1400 rev/min. 1) For a 11.8mm--diameter drill bit turning at a constant 1400 rev/min , find the maximum linear speed of any part of the bit.
2) Find the maximum radial acceleration of any part of the bit.

a) v max = 0.1376 m,/s

b) a max = 3.212 m/s^2

Explanation:

a) To find the maximum linear sped of any part of the bit, you use the following formula:

      (1)

v: linear speed

w: angular velocity of the bit = 1400 rev/min

r: distance to the center of the bit

You can observe that for r=rmax you obtain the maximum linear speed.

rmax = diameter/2 = 11.8mm/2 = 5.9mm

Before you replace the values of w and r in the equation (1), you convert to appropriate units:

Then, you obtain:

the maximum linear speed of the bit is 0.1376 m/s

b) The maximum radial acceleration is given by:

the maximum radial acceleration is 3.212 m/s^2

it is b. absorbs thermal energy