Question

A flywheel having constant angular acceleration requires 4.00 ss to rotate through 164 radrad . Its angular velocity at the end of this time is 106 rad/srad/s . Find the angular velocity at the beginning of the 4.00 ss interval; the angular acceleration of the flywheel. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Rotation of a bicycle wheel.

Answer 1

Answer:

$\omega '=-13.5rad/s$

Explanation:

From the question we are told that:

Time $t=4sec$

Angular displacement $\theta= 161 rad$

Final Angular velocity  $\omega = 100 rad / s$

Let

Angular acceleration $\alpha$  

Generally the equation for Initial Angular velocity  $\omega '$ is mathematically given by

$-\omega '^2=2 \alpha \theta -\omega^2$

$\omega '^2= \alpha 328 +11236$

Also,Initial Angular velocity  $\omega '$ is mathematically given by

$\omega '=\omega - \alpha t$

Therefore substitution

$-\omega '^2=2 \alpha \theta -\omega^2$

$\omega '=\omega - \alpha t$

$(\omega - \alpha t)^2=2 \alpha \theta -\omega$

$-16\alpha^2+848\alpha+11236= \alpha 328 -11236$

$16\alpha^2-520\alpha=0$

$\alpha=29.875rads/s^2$

Substitution in the 2nd equation for Initial Angular velocity  $\omega '$

$\omega '=106-(29.875rads/s^2*4)$

$\omega '=-13.5rad/s$