How Long Does It Take for a Phonograph Record to Stop Spinning?

[nautica]

A phonograph record slows from an initial 45 rpm at a rate of .05 rad/s^2.

a) how long does it take to come to rest?

orig rotational velocity = 45 rpm = 4.71 rad/sec
acc = -.05 rad/s^2

0 = 4.71 rad/s + (-.050 rad/s^2) t
t = 94.2 s

b) How many revolutions does it make before stopping?

(w + w)/2 = (4.71 rad/sec)/2 = 2.355 rad/s * 94.2 s = 221.84 rads =
35.31 rev

Last one for the week. How does this look?

Thanks agaiin
Nautica

 

[arcnets]

I think it's correct.

Here's a shorter and more precise way to do (b):

Without slowing down, you get
45*94.2/60 = 70.65 revolutions.
When slowing down, you know the answer is half of that:
35.325 revolutions.

 

[nautica]

Thanks, but for some reason the longer version makes more sense to me.

Nautica