1. Representations.
Sketch graphs of the angular acceleration, angular velocity, and angular position vs. time.
Section 5.6 Nonuniform Circular Motion
An object moving in a circle with a non-constant speed is said to undergo nonuniform circular motion. Since the speed is changing, the object must have a non-zero tangential acceleration. The magnitudes of the tangential and angular acceleration are related by \(\alpha = \frac{a_t}{r}\text{.}\) An object undergoing nonuniform circular motion still has a centripetal acceleration, which will change as the speed changes. When using the Law of Motion to relate acceleration to the net force, the entire acceleration vector must be used, including both the tangential and centripetal components.
Exercises Activity - The Go-kart
You are on a Go-kart at a circular track such that the Go-kart’s angular acceleration is a constant \(0.6 \frac{\text{rad}}{\text{s}^2}\text{.}\) Your initial angular speed is \(-1.2 \frac{\text{rad}}{\text{s}}\text{.}\)
2. Calculations.
Find equations for the angular position, angular velocity, and angular acceleration as functions of time.
3. Understanding.
How does the centripetal acceleration of your Go-kart change as you go?
