A three-inch-diameter pulley on an electric motor that runs at 1700 revolutions per minute is connected by a drive belt to a five-inch-diameter pulley that turns the mandrel on a woodworking lathe. Find the angular speed (in radians per minute) of each pulley.
A)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute
B)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute
C)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute
D)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute
E)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute

Question

A three-inch-diameter pulley on an electric motor that runs at 1700 revolutions per minute is connected by a drive belt to a five-inch-diameter pulley that turns the mandrel on a woodworking lathe. Find the angular speed (in radians per minute) of each pulley.
A)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute 
B)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute 
C)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute 
D)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute 
E)three-inch-diameter pulley: radians per minutefive-inch-diameter pulley: radians per minute

Quizplus · Accepted Answer

The angular speed of a pulley is given by the formula $\frac{	ext{linear speed}}{	ext{radius}}$. Since the two pulleys are connected by a belt and must maintain the same belt speed, the linear speed of the two pulleys must be equal. Therefore, we have:

Angular speed of three-inch pulley $= \frac{	ext{linear belt speed}}{1.5}$ (since radius is half of diameter)
Angular speed of five-inch pulley $= \frac{	ext{linear belt speed}}{2.5}$

We are given that the electric motor runs at 1700 revolutions per minute. Since the three-inch pulley is directly connected to the motor, its angular speed must also be 1700 revolutions per minute. To find the angular speed of the five-inch pulley, we can use the fact that the two pulleys must maintain the same belt speed. The circumference of the three-inch pulley is $2\pi(1.5) = 3\pi$ inches, and the circumference of the five-inch pulley is $2\pi(2.5) = 5\pi$ inches. Therefore, the linear belt speed is equal to $3\pi 	imes 1700$ inches per minute. Plugging this into the formulas above, we get:

Angular speed of three-inch pulley $= \frac{3\pi 	imes 1700}{1.5} \approx 11ec1854\_fd7d\_9d34\_acfc\_71390db1a5da\_TBX8702\_11$ radians per minute
Angular speed of five-inch pulley $= \frac{3\pi 	imes 1700}{2.5} \approx 11ec1854\_fd7d\_9d35\_acfc\_eff0cbc3a4d2\_TBX8702\_11$ radians per minute

Therefore, the answer is choice A.

A Three-Inch-Diameter Pulley on an Electric Motor That Runs at 1700