Angular acceleration

  • Thread starter Wes Turner
  • Start date
  • #1
66
14

Homework Statement


A computer disk starts from rest, then speeds up with angular acceleration of 190 rad/s^2. until it reaches its final speed of 7200 rpm. How many revolutions will it have made 10.0 secs after starting up?

Homework Equations


w = w0 + at
rps = rpm / 60
1 rev = 2*pi rad
1 rad = 1/(2*pi) rev
190 rad/s^2 = (190/(2*pi)) rev/s^2 = 30.24 rev/s^2
7200 rpm = 7200/60 rps = 120 rps

The Attempt at a Solution


Calculate the time it will take to get up to full speed.
w = w0 + at
7200 rpm = 0 rpm + 190 rad/s^2 * t
120 rps = 0 rps + 30.24 rev/s^2 x t
t = 120 rev/s / 30.24 rev/s^2 = 3.97 s

Over the first 3.97 s, it the angular velocity increases linearly, so the average is 120 rps/2 = 60 rps.
At 60 rps for 3.97 sec, it completes 238 revolutions.

That leaves 10 s - 3.97 s = 6.03 s x 120 rps = 724 revolutions.

Then 238 + 723 = 962 total revolutions in the first 10 seconds.

Is that correct?

Thanks
 

Answers and Replies

  • #2
stockzahn
Homework Helper
Gold Member
498
137
Yes, correct solution. But instead of

Over the first 3.97 s, it the angular velocity increases linearly, so the average is 120 rps/2 = 60 rps.

you could have calculated it with ##φ=\ddot{φ}\frac{t^2}{2}##.
 

Related Threads on Angular acceleration

  • Last Post
Replies
2
Views
1K
Replies
6
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
3
Views
830
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
11
Views
1K
Top