Question

A thread is being pulled off a spool at the rate of 61.9 cm per sec. Find the radius of the spool if it makes 132 revolutions per min.

Answer 1

4.478 cm

Explanation:

You want the radius of a spool making 132 revolutions per minute when its tangential speed is 61.9 cm per second.

Circumference

In one minute, the length of thread removed from the spool will be ...

(61.9 cm/s) × (60 s) = 3714 cm

This represents 132 revolutions, so each revolution is ...

(3714 cm)/(132 rev) = 28 3/22 cm/rev

This circumference is 2π times the radius:

C = 2πr

r = C/(2π) = (28 3/22 cm)/(2π) ≈ 4.478 cm

The radius of the spool is about 4.478 cm.