• Support PF! Buy your school textbooks, materials and every day products Here!

Rotational motion- steam engine

  • Thread starter fruitl00p
  • Start date
94
0
1. Homework Statement

The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.35 rad/s^2. It accelerates for 33.1 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 47.5 s after it begins rotating.

2. Homework Equations

1. w=wi +alpha(time)

2. theta - theta(initial) = 1/2(w +wi)t

3. The Attempt at a Solution
I have attempted this problem several times and keep getting the answer wrong!!! (note: I do not know the correct answer for this particular problem)

First I used equation 1 to find the constant angular velocity. Then, since I know that constant velocity means zero acceleration, I used equation 2 to find the total angle. What am I doing wrong? Please help!:confused:
 

Andrew Mason

Science Advisor
Homework Helper
7,536
317
1. Homework Statement

The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.35 rad/s^2. It accelerates for 33.1 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 47.5 s after it begins rotating.

2. Homework Equations

1. w=wi +alpha(time)

2. theta - theta(initial) = 1/2(w +wi)t
It would help to graph the angular speed as a function of time. The area under the graph is what you are trying to calculate.

If it starts at [itex]\omega = 0[/itex] then [itex]\omega = \alpha t[/itex] and:

[tex]\theta_1 = \frac{1}{2}\alpha t_1^2[/tex] (angle after 33.1 seconds)

[tex]\theta_2 = \alpha(t_1) (t_f - t_1)[/tex] (increase in angle to t= 47.5 seconds)

which is essentially what you have already figured out. Just add those two equations to get [itex]\theta = \theta_1 + \theta_2 [/itex] and solve.

AM
 

Mentz114

Gold Member
5,422
289
There are 2 phases - 33.1s of acceleration and 14.4s of constant velocity.
You must calculate the number of turns for each phase and add them.
Adapt the well known relations

distance = 1/2*acc*time^2
distance = velocity*time

to the angular case.
 
94
0
thank you very much, I got the answer correctly. :smile:
 
2
0
I am actually using θ1= ½ αt12 and θ2=α (t1)(tf-t1) and adding both angles together but I am not getting the answer right??

thanks
 
Last edited:
2
0
aha, the answer was in radians, not degrees
 

Related Threads for: Rotational motion- steam engine

  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
18
Views
5K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
10K
  • Last Post
2
Replies
37
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
257

Recent Insights

Top