Reply #13: No... [View All]

No, we are not too concerned with an actual numerical value for angle theta. We just want to know, firstly, what angle theta is as a function of time, and, secondly, what the derivative(s) of this function is(are). In this problem we are just looking for the first derivative, that is, what the rate of change of angle theta is with respect to time (d/dt). The derivative of the arctan function is as follows, which might be listed somewhere in your textbook:

d/dt arctan (t) = 1 / (t^2 + 1)

And of course don't forget to apply the chain rule for the argument (t) of the arctan function when taking its derivative.

Anyway, the function of s(t) = 60*t^2, if you graph it out, is a parabola opened upwards, with the very bottom located at (0,0). What the derivative of this function tells you, is what the slope of this function is at whatever point in time you are looking at, say at t = 10 seconds. This value will of course vary, depending on where you are on the curve. The units for the time rate of change for angle theta will be radians / second (or radians per second).