A 'SawStop' table saw quickly stops the rotation of the saw blade when it comes in contact with a capacitive object (such as a finger), to prevent accidents. A carpenter pushes a piece of plywood through the table saw at a speed of 5 cm/s. The stopping mechanism is triggered (don't worry the carpenter is safe!). (A)The circular saw blade has a radius 12 cm and rotates at 4,000 rpm. If the rotation of the saw stops 2 ms (0.002 s) after contact with the blade, what is the angular acceleration as the blade slows down, assuming that the acceleration is constant (it will be very large and damage parts of the saw in the process).
(B) What angle will the saw blade rotate through as it comes to stop?
(C) If the blade stops rotating in 2.0 ms, the piece of wood would only travel 0.1 mm, about the thickness of a piece of paper, before the saw blade has stopped rotating (just a scratch)!