Question

The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.33 rad/s2. It accelerates for 27.9 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 53.5 s after it begins rotating.

Answer 1

We first to know that if the wheel rotates from rest means that at t=0 the velocity and the angle rotated is 0.

Then, we know:

`\alpha = 1.33 = (dw)/(dt)`

Integrating 2 times, we have:

`w = 1.33t\\angle =0.665t^(2)`

For the first 27.9 s, we have:

w = 37.107 rad/s

angle = 517.6426 rad

For the next seconds, according to the text, the angular velocity is constant so

w = 37.107 rad/s and hence, integrating:

`angle =37.107t`

Then, the time remaining is:

53.5 - 27.9 = 25.6

So for the next 25.6 seconds we have:

`angle = 37.107*25.6=949.9392 rad`

Finally, we add the 2 angles and we have as a result:

`angle = 517.6426+949.9392=1467.5818`