Answer to Question #285513 in Physics for Mike

Question

An old-style elevator is connected to a counterweight by a cable that passes 

over a rotating disk that is 3.7 meters in diameter. With the cable not slipping and turning with the disc, the elevator is raised and lowered by turning the disc. a. How many turns should the disc make to raise the elevator at 0.5 m/s. b. The elevator should accelerate at a quarter of the acceleration due to gravity 

to start the elevator moving. Calculate the disc's angular acceleration. c. How many revolutions has the disc spun when it has raised the elevator 5 

m between floors? 

Answer 1

a. The number of turns:

$$\omega=2v/d=0.27\text{ rad/s, or 0.04 turns/s}.$$

b. The angular acceleration:

$$\alpha=2a/d=g/(2d)=1.32\text{ rad/s}.$$

c. The number of revolutions:

$$n=\dfrac{H}{\pi d}=0.43.$$