How? The motor of a table saw is rotating at 3450 rev/min. A pulley attached to

Question

How?

The motor of a table saw is rotating at 3450 rev/min. A pulley attached to the motor shaft drives a second pulley of half the diameter by means of a V-belt. A circular saw blade of diameter 0.208 m is mounted on the same rotating shaft as the second pulley.

The operator is careless and the blade catches and throws back a small piece of wood. This piece of wood moves with linear speed equal to the tangential speed of the rim of the blade. What is this speed? Calculate the radial acceleration of points on the outer edge of the blade to see why sawdust doesn't stick to its teeth.

Explanation / Answer

The mechanical advantage of the motor to blade shaft means the blade is rotating at
2*3450 rpm

convert that into rad/s

2*3450*2*pi/60 rad/s=230*pi rad/s

a)

the tangential speed on the blade is
v=230*pi*0.208/2 m/s
v= 75.14 m/s

b)

the acceleration at the outer edges is

a=v^2/r

a=75.14^2*2/0.208

a=54288 m/s^2

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