Rotational motion- steam engine

In summary, the flywheel of a steam engine rotates for 47.5 seconds and has turned through an angle of 1.35 radians.
  • #1
fruitl00p
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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.

Homework Equations



1. w=wi +alpha(time)

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

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:
 
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  • #2
fruitl00p said:

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.

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
 
  • #3
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.
 
  • #4
thank you very much, I got the answer correctly. :smile:
 
  • #5
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:
  • #6
aha, the answer was in radians, not degrees
 

FAQ: Rotational motion- steam engine

1. What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. It is characterized by the rotation of the object, rather than its linear movement.

2. How does a steam engine use rotational motion?

A steam engine uses rotational motion to convert the linear motion of a piston into the rotational motion of a crankshaft. This rotational motion is then used to power machinery, such as trains or factories.

3. What is the role of the flywheel in a steam engine?

The flywheel in a steam engine is a heavy wheel that is attached to the crankshaft. Its main function is to store energy and provide a consistent rotational speed, as the steam engine's power output fluctuates.

4. What are the main components of a steam engine?

The main components of a steam engine include a boiler, a cylinder, a piston, a crankshaft, a flywheel, and valves. The boiler produces steam, which then enters the cylinder and pushes the piston, causing the crankshaft to rotate and the flywheel to turn.

5. What are some advantages of using a steam engine?

Some advantages of using a steam engine include its ability to provide consistent power and its efficiency in converting heat energy into mechanical energy. It also played a significant role in the Industrial Revolution, powering various machines and revolutionizing transportation.

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