Rotational Kinematics Practice Test

A wheel with moment of inertia $I=1.2\ \text{kg·m}^2$ must speed up from $\omega_0=5.0\ \text{rad/s}$ to $\omega_f=17\ \text{rad/s}$ in $t=4.0\ \text{s}$ under a constant net torque (friction included). Key equations: $\alpha=(\omega_f-\omega_0)/t$ and $\tau=I\alpha$. Using the given conditions, what is the torque required to achieve this change?

A disk with moment of inertia $I=0.30\ \text{kg·m}^2$ is acted on by a constant torque $\tau=1.5\ \text{N·m}$ for $t=2.0\ \text{s}$, starting from rest; friction is negligible. Key equations: $\tau=I\alpha$ and $\theta=\tfrac12\alpha t^2$. Using the given conditions, calculate the total angular displacement during the 2.0 s interval.