Hello, turkeyy!

As a cable is pulled from a large spool, it unwinds in layers of constant radius.

If the cable is pulled at a steady 6 ft/sec, use the equation

to find how fast (radians/sec) the spool is turning when the radius is 1.2 ft. Code:

* * *
* *
* *
* *
* O *
* * *
* | * *
| θ *
* 1.2 | * *
* | o Q
* | *
* o * → → → → → →
P 6 ft/s

The cable is pulled horizontally at 6 ft/sec.

Then point is moving around the circle at the same rate.

We have: .

From , we have: .

Differentiate with respect to time: .

Since , we have: .