FIGURE EX4.23 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?

Key Concepts

Angular Velocity

Angular velocity is a measure of how quickly an object rotates around a central point, expressed in radians per second (rad/s). It indicates the rate of change of the angular position of the object. In circular motion, it is crucial for determining how far the object travels along its circular path over time.

Area Under the Curve

In a graph of angular velocity versus time, the area under the curve represents the total angular displacement of the object. This area can be calculated using geometric shapes, such as rectangles and triangles, depending on the shape of the graph. The total angular displacement can then be converted into revolutions by dividing by 2π radians.

Revolutions

A revolution refers to one complete turn around a circular path, equivalent to an angular displacement of 2π radians. To find the number of revolutions made by an object, one must calculate the total angular displacement from the angular velocity graph and divide that value by 2π. This concept is essential for understanding the relationship between linear and angular motion.