2.3: Angular Motion

Angular motion, also known as rotary motion, occurs when a body or object moves along a circular path around a fixed point known as the axis of rotation. Unlike linear motion, where all parts of an object move the same distance in the same direction, during angular motion, different parts of the body travel different distances in the same amount of time. In sports, angular motion is incredibly common, as nearly all human movement is generated by the angular rotation of bones around joint axes. Examples include a gymnast spinning around a high bar, a figure skater executing a spin, or a diver performing a somersault.

To understand how angular motion is created, one must look at the concept of torque, or eccentric force. A linear motion is caused by a direct force applied through an object’s center of mass. In contrast, angular motion is created when an eccentric force is applied outside the object's center of mass. This turning effect is called torque. The magnitude of torque depends on the size of the force applied and the length of the moment arm, which is the perpendicular distance from the axis of rotation to the line of action of the force. For example, a footballer kicking a ball puts spin on it by striking it off-center, applying a torque that initiates angular motion.

To describe angular motion, specific kinematic quantities are used, which parallel linear motion but are measured in angles (degrees or radians) rather than meters. Angular displacement measures the smallest change in angle between the starting and finishing position of a rotating body. Angular velocity describes the rate of change of angular displacement over time, essentially measuring how fast something is spinning. Finally, angular acceleration measures the rate at which a spinning object speeds up or slows down its rotation. For a gymnast performing a giant swing on the high bar, their angular velocity will change throughout the circle depending on gravity and the torque they generate.

A fundamental concept in angular motion is the relationship between the moment of inertia and the angular velocity, governed by the conservation of angular momentum. Angular momentum is the quantity of angular motion possessed by a body and is calculated by multiplying the moment of inertia by the angular velocity. According to the law of conservation of angular momentum, this total quantity remains constant unless acted upon by an external torque. Because momentum cannot change mid-air, an athlete can manipulate their spinning speed by changing their body shape.

The moment of inertia is an object’s resistance to rotation and depends entirely on the mass of the body and how far that mass is distributed from the axis of rotation. When a diver pulls their arms and legs tight into a tuck position, they move their mass closer to the axis of rotation, drastically reducing their moment of inertia. Because angular momentum must remain constant, this reduction in resistance causes a massive increase in angular velocity, making them spin rapidly. Conversely, when they extend their limbs out straight into a layout position just before entering the water, they increase their moment of inertia, which automatically decreases their angular velocity, allowing them to stop the spin and enter the pool cleanly.