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Chapter 10: Problem 14

A 32 -cm-diameter circular saw blade spins at \(2100 \mathrm{rpm}\). How fast would you have to push a straight hand saw to have the teeth move through the wood at the same rate as the circular saw teeth?

Short Answer

Expert verified
To match the speed of the circular saw's teeth, the hand saw must be moved with a speed of \(3.14 \times 32 \times 2100\) cm/min.

Step by step solution

01

Calculate the Circumference of the Circular Saw Blade

The first step is calculating the circumference of the circular saw blade as the teeth of a circular saw move in a circular direction. The formula for the circumference is \(C = \pi D\), where \(D\) is the diameter of the circular saw blade given as 32 cm. So, \(C = 3.14 \times 32\) cm.
02

Convert the RPM into Linear Speed

We know the rotational speed of the blade to be 2100 rpm. The teeth of the saw blade cover one circumference per revolution. Hence, in one minute (2100 revolutions), the linear distance covered is given by \(C \times RPM = 3.14 \times 32 \times 2100\) cm per minute.
03

Convert Linear Speed into Hand Saw Speed

The speed calculated previously is the linear speed of the circular saw's teeth. To match this speed, the hand saw would have to be moved at the same speed. Therefore, the speed to push a straight hand saw is the same as the linear speed of the circular saw teeth. That is, it equals \(3.14 \times 32 \times 2100\) cm/min.

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