ANGULAR MOTION CONCEPTS

Torque --» A rotation or turning effect that produces angular motion around a central point.

• Formula: T = Fd where T = torque, f = force, and d = force arm (the perpendicular distance from axis to application of force.

Angular Displacement --» degrees traveled (θ = theta) or in radians (1 rad = 57.2957° degrees; 6.28 rad in a circle)

Angular Velocity --» The speed in degrees per unit of time an object is moving  in an arc.

• Formula: w = θ/t where w = angular velocity, θ = degrees or radians (1 rad = 57.3 degrees), t = time, A positive value is equal to acceleration, a negative value deceleration.

Angular Acceleration --» Is the change in angular velocity over a specific unit of time.

• Formula: Angular Acceleration  (α = alpha) α = w2 - w1/t where w2 = final angular velocity, w1 = initial angular velocity, & t = time.

Rotational Inertia --» Is an object's resistance to change in rotational state of motion.

• Formula: Rotational Inertia = (m)(r²) or I = mr². where I = inertia, m = mass, & r = radius to center of gravity.
• Formula for segmented objects: I = (m)(k²) where k = radius of gyration (the distribution of mass from the point of rotation, the axis).

Angular Momentum --» Quantity of an object's angular motion. The greater this quantity the greater its resistance to its motion state.

• Formula: L = (m)(k²)(w) where m = mass, k = radius of gyration, w = angular velocity.

Conservation of Angular Momentum --» Angular momentum of an isolated system will remain the same regardless of any movements or torques that are produced internal to the system, as long as no external torque is applied to the system.

• For example the ice skater spin, when the arms are out the body has low angular velocity (rotating slowly). As the skater pulls the arms to the body the angular velocity increases (rotation speeds up).

Angular Impulse --» Formula: Change in angular momentum = (T)(t) where T = external torque & t = time. Another form is (change in L) = (Iw₂) - (Iw₁) where L is a change in angular momentum, I = angular inertia, w2 = ending angular velocity, & w1 = beginning angular velocity.
 

Order of Importance - Angular acceleration, angular velocity, & linear translation.

•  First Angular acceleration and velocity since this maximizes the effect of muscle force, then linear translation of the angular movement (e.g., opening up the limb).

• In human motion, typically angular velocity is maximized first then at the proper timing of the body or limbs are elongated (opened up) to enhance linear motion/velocity.