2000010805

A flywheel rotates such that it sweeps out an angle at the rate of $$\phi =4t^2,$$ where an angle $\phi$ is measured in radians and time $t$ is measured in seconds. At what time is instantaneous angular velocity of the flywheel equal to $36\frac{\mathrm{rad}}{s}$? (Hint: Instantaneous angular velocity can be expressed as the derivative of the function $\phi (t)$ with respect to time: $\omega (t)=\frac{\mathrm{d}\phi }{\mathrm{d}t}$.)