Question

A radial saw has a blade with a 6-in. radius. Suppose that the blade spins at 1100 rpm.
(a) Find the angular speed of the blade in rad/min.
(b) Find the linear speed of the sawteeth in ft/s.

Answer 1

I can help!

Answer 2

What do you think the answer is?

Answer 3

I'm really not sure at all.

Answer 4

@flcon04

Answer 5

Dimensional Analysis!

Radius = 6"
Circumference= 2 * 6" * \(\pi\) = \(12\pi\)"

\(\dfrac{1100\;rev}{1\;min}\cdot\dfrac{2\pi\;rad}{1\;rev}\)

\(\dfrac{1100\;rev}{1\;min}\cdot\dfrac{12\pi\;in}{1\;rev}\cdot\dfrac{1\;ft}{12\;in}\cdot\dfrac{1\;min}{60\;sec}\)

Think very, very hard on this.

Answer 6

Notice how when you set up the way @tkhunny did it, all the units cancel nicely, leaving you only with your desired unit at the end? (he has provided two equations, one for each part of the problem) If you screw up, you end up with some sort of nonsense unit, like maybe "rev in^2/ft" which is your tip-off that you've bungled something. It's a little more work, but well worth the effort, as mistakes doing unit conversions (which is essentially all this problem involves) are very easy to make. Also catches many mistakes where you needed to do a unit conversion, but didn't!

This approach is so powerful that it is even possible to derive formulas in some cases based on reasoning about the units.