Centripetal Motion and Rotation
In physics, centripetal motion is the motion of an object traveling along the circumference (or perimeter) of a circle at a constant speed. However, even though the speed is constant throughout the entirety of the circular arc, the velocity changes, because the speed is constantly changing direction. This means that there is a constant acceleration throughout the motion. Without the acceleration, the object spinning would simply fly forward. Centripetal refers to everything pointing inwards, and centrifugal refers to everything pointing outwards. You feel a centrifugal force when you take a turn in a car, as you feel a pull outside the curve.
Centripetal acceleration can once again be calculated using Newton’s 2nd law, but forces need to be on the centripetal plane, or pointed inwards/outwards of the circle, not along it. Centripetal acceleration is always pointed inwards, allowing the velocity to stay along the circle instead of staying straight. Centripetal acceleration can also be calculated with v²/r.
When dealing with rotational motion, you cannot use typical cartesian variables for physical concepts. Instead of displacement being in terms of x or y, it is in terms of θ (theta), or the angle traveled, usually measured in radians. The angular (rotational) versions of velocity and acceleration are ω (omega) and α (alpha) respectively which can be found by dividing the value by the radius. Time is measured as period, which is the time it takes to go around the circle once.
Inertia, I, is a concept that represents resistance to acceleration. As inertia increases, angular acceleration decreases. This follows the pattern of Newton’s second law when translated to circular motion, which becomes τ = Iα, where τ is torque, which will be covered in the work section of mechanics. All shapes have different inertial values, all of which depend on radius and mass. Think of how a solid sphere spinning has different acceleration than a solid rod spinning around one of its ends.
