At time $t = 0$, a disk starts from rest and begins spinning about its center with a constant angular acceleration of magnitude $\alpha$. At time $t_f$, the disk has angular speed $\omega_f$. Which of the following expressions correctly compares the final angular displacement $\theta_f$ of the disk at time $t_f$ to the angular displacement $\theta_{1/2}$ at time $\dfrac{t_f}{2}$?

Question

At time $t = 0$, a disk starts from rest and begins spinning about its center with a constant angular acceleration of magnitude $\alpha$. At time $t_f$, the disk has angular speed $\omega_f$. Which of the following expressions correctly compares the final angular displacement $\theta_f$ of the disk at time $t_f$ to the angular displacement $\theta_{1/2}$ at time $\dfrac{t_f}{2}$?(a) $\theta_f = \dfrac{\theta_{1/2}}{4}$
, (b) $\theta_f = \theta_{1/2}$
, (c) $\theta_f = 2\theta_{1/2}$
, (d) $\theta_f = 4\theta_{1/2}$
:

Rita · Accepted Answer

$\boxed{\theta_f = 4\theta_{1/2}}$

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