Question

A measuring tape unwinding from a drum of radius r.The center of the drum is not moving; the tape unwinds as its free endis pulled away from the drum. Neglect the thickness of the tape, sothat the radius of the drum can be assumed not to change as the tapeunwinds. In this case, the standard conventions for the angularvelocity 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).Assume that the function x(t) represents the length of tape that has unwound as a function of time. Find θ(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.Express your answer (in radians) in terms of x(t) and any other given quantities.θ(t)=x(t)/r

Answer 1

θ = x / r

Step-by-step explanation:

This is an exercise that relates the angular and linear quantities, in the statement they indicate the relationship of the speeds

v = w r

Linear and rotational speeds are defined

v = x / t

w =θ / t

let's substitute in the first equation

x / t = (θ / t) r

x = θ r

θ = x / r

It is important to note that the angles must be measured in radians