Find theta(t), the angle through which the drum will have rotated, as a function of time.?

Question

Consider a measuring tape unwinding from a drum of radius r. The center of the drum is not moving; the tape unwinds as its free end is pulled away from the drum. Neglect the thickness of the tape, so that the radius of the drum can be assumed not to change as the tape unwinds. In this case, the standard conventions for the angular velocity omega and for the (translational) velocity v of the end of the tape result in a constraint equation with a positive sign (e.g., if v>0, that is, the tape is unwinding, then omega > 0 also).

http://session.masteringphysics.com/problemAsset/1011025/23/MRB_cn_a.jpg

Assume that the function x(t) represents the length of tape that has unwound as a function of time. Find theta(t), the angle through which the drum will have rotated, as a function of time.

Express your answer (in radians) in terms of x(t) and any other given quantities.

Answer 1

Well x(t) = r*theta(t)

So, theta(t) = x(t)/r after rearranging the equation to solve for theta(t).