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

The second pulley, with half the diameter of the first, must have twice the angular velocity, and this is the angular velocity of the saw blade.

r1w1 = r2w2

3450 rev/min = 361.283 rad/s

v = r2w2

v = r1w1

r1 = 0.208/2 = 0.104m

v = 75.15 m/s^2

part b )

alpha = w^2*r

alpha = 5.43 x 10^4 m/s^2

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