Revolutions from angular velocity vs time graph| Circular Motion| Physics

The figure shows the angular-velocity-versus-time graph for a particle moving in a circle.

A) How many revolutions does the object make during the first 4.0 s?



ANSWER: n=9.5

The total number of radians made by the object is the area under the graph. Based on the given graph, the total number of radians is 

\theta _{rad}=60\:radians

Convert this to revolutions, knowing that 2π radians is equal to 1 revolution. 

revolutions=60\:rad\times \frac{1\:rev}{2\pi }=\frac{60}{2\pi }rev=9.5\:rev