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

Answer:

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:

$\alpha = 1.33 = \frac{dw}{dt}$

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:

$angle = 517.6426+949.9392=1467.5818$