Question

The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.27 rad/s^2. It accelerates for 27.5 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 66.1 s after it begins rotating.

Answer 1

With a constant angular acceleration of 1.27 rad/s^2 and acceleration of 27.5 s, is mathematically given as

$\theta = 1848 radians$

What is the total angle through which the wheel has turned 66.1 s after it begins rotating?

Generally, the angular velocity  is mathematically given as

w2 = 0 + 1.27*27.9

w2 = 35.43 rad/s

Therefore

$\theta1 = 0.5*1.27*27.9*27.9$

$\theta2 = w2*(66.1-27.9)\\\\\ \theta = \theta1 + \theta2$

$\theta = 1848 radians$

In conclusion, the total angle is

$\theta = 1848 radians$

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