# Rotational motion- steam engine

## 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!

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Andrew Mason
Homework Helper

## 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 $\omega = 0$ then $\omega = \alpha t$ and:

$$\theta_1 = \frac{1}{2}\alpha t_1^2$$ (angle after 33.1 seconds)

$$\theta_2 = \alpha(t_1) (t_f - t_1)$$ (increase in angle to t= 47.5 seconds)

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

AM

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.

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

to the angular case.

thank you very much, I got the answer correctly.

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

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