A pulley 12 inches in diameter makes 150 complete rotations per minute. What is the linear velocity, in feet/sec, of a cable attached to the pulley? In feet/sec. -5/2 pi rads/sec

To find the linear velocity of a cable attached to the pulley, we first need to calculate the circumference of the pulley. The diameter of the pulley is 12 inches, so the radius is 6 inches. The circumference \( C \) of the pulley is given by:<br /><br />\[ C = 2\pi \times \text{radius} = 2\pi \times 6 = 12\pi \text{ inches} \]<br /><br />The pulley makes 150 complete rotations per minute. Therefore, the distance traveled by the cable in one minute is:<br /><br />\[ 150 \times 12\pi \text{ inches} \]<br /><br />To convert this distance to feet, we divide by 12 (since there are 12 inches in a foot):<br /><br />\[ \frac{150 \times 12\pi}{12} = 150\pi \text{ feet per minute} \]<br /><br />Now, to convert this to feet per second, we divide by 60 (since there are 60 seconds in a minute):<br /><br />\[ \frac{150\pi}{60} = \frac{15\pi}{6} = \frac{5\pi}{2} \text{ feet per second} \]<br /><br />Therefore, the linear velocity of the cable is \(\frac{5\pi}{2}\) feet per second.