## Physics (10th Edition)

The angular displacement of the wheel is $+270.8rad$
We are given final angular velocity $\omega=+1.88rad/s$, angular acceleration $\alpha=-5.04rad/s^2$ and duration $t=10s$ The angular displacement of the wheel is $$\theta=\omega_0t+\frac{1}{2}\alpha t^2$$ We also know that $\omega_0=\omega-\alpha t$ $$\theta=(\omega-\alpha t)t+\frac{1}{2}\alpha t^2$$ $$\theta=\omega t-\frac{1}{2}\alpha t^2=+270.8rad$$