Chain Rule of Differentiation
Recall that when taking derivatives of a differentiable function \(f = f(\theta)\) whose argument is also a differentiable function \(\theta=g(t)\) then \(f=f(g(t))=h(t)\) is a differentiable function of \(t\) and
\(\frac{df}{dt}=\frac{df}{d\theta}\frac{d\theta}{dt}\)
Note that this is only in the case of circular motion, where \(r\) is a constant in time. Otherwise, our derivative of \(f\) would also have a \(\frac{df}{dr}\frac{dr}{dt}\) term.
Radians
One way to measure an angle is in radians. A full circle has \(2\pi\) radians. This week, we will use radians to measure the angles, so all angles will have units of radians, angular velocity will have units of radians/s, and angular acceleration will have units of radians/s\(^2\). If we multiply these by a distance, such as \(r\), the units will be m, m/s, or m/s\(^2\).
External References