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

Question

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.

A) 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?

B)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

a)

First we will convert 3450 rev/min into rad/s

w =3450*2pi/60 =361.1rad/s

From the given we can say that the angualr velocity of the econd pulley will be double that of the first pulley because its diameter is half that of the first one

Now the speed of the wood is v =2wr =2*361.1*0.208/2 =75.1088m/s

b)

Now the radial acceleration of points on the outer edge of the blade to see why sawdust doesn't stick to its teeth is given by

aradial =(2w)2*r =4*(361.1)2*(0.208m/2) =54243.575m/s2

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