Angular Kinematics

Spatial Angular Kinematics

angular position, distance, and displacement

Angular Positions

orientation of a line w/ another line or plane; in radians; theta, s, and r

theta

angle in radians; arc length/r = s/r

s

arc length

r

radius

Angular Distance

radians; total angular amount travelled

Angular Displacement

radians; change in abs. angular pos. experienced by rotating line; delta theta; angle formed between final and initial pos.; range of motion

Measuring Angles

angle between body segments is important; measured in degrees; joint angles; body segment angle of orientation

What tools are used to measure angles?

goniometer, videos, and motion capture

Joint Angles

measured as segment movement away from anatomical position; SAP

What is regarded as 0 degrees?

straight, fully extended position at a joint

Body Segment Angle of Orientation

w/ respect to a fixed line of reference (horizontal or vertical); ex. trunk angle w/ respect to vertical is often a quantity of interest in studies of lifting as related to low back pain

Angular Velocity

rad/s; rate of change of angular displacement; angular displacedment/time

Angular Acceleration

rad/s²; rate of change of angular velocity; angular velocity/time

What are vectors?

angular displacement, velocity, and acceleration

What is + when in the direction of motion?

displacement and velocity

Rotation about a Fixed Axis

tangential and normal; perpendicular to each other

Tangential

velocity tangent to motion path = linear velocity acceleration direction same if v increasing

Normal

acceleration is always directed inward

What can produce linear motions?

rotations

What can be described as linear?

rotational motion

Linear Motion

delta s, v, and a

Angular

delta theta, omega (w), and alpha

Increaisng the radius does what?

increases the linear distance traveled by that point during angular motion; s=rtheta

increased angular velocity increases the linear velocity

ex. the greater the angular velocity of a baseball bat, the farther a struck ball will travel, other conditions being equal

Uniform Circular Motion

angular velocity of rotational object about a fixed axis is constant → v=rw is constant, at=0, and an=rw² is constant

Torque

turning effect on a body measured as the product of force and moment arm length

Mass Moment of Inertia

Io=mr²

Inertia

resistance to change; in humans → resistance to ac/deceleration; tendency for current state of motion to be maintained, regardless of static dynamic

What is required to change inertia?

force; ex. muscle forces or external forces

Greater mass leads to what?

greater inertia; needs more force to change it’s state

Mass Moment of Inertia

resistance to angular acceleration (rotational motion); based on mass/distance the mass is distributed from the axis of rotation; sum of products pf particle’s mass (m) and radius of rotational (r) for that particle squared; mr² in kg*m62

Angular Work

work done by a force applied to a rotating body; product of force and corresponding angular displacement; W=Fts where s=rtheta, W=Ftrtheta but Ftr=m, and W-Ntheta for constant moment

Angular Work Energy Theorem

net angular work done, W, on an object to rotate it from position 1 to position 2 is equal to the change to the change in angular kinetic energy; W=(1/2)I(w2² - w1²)

Angular Power

rate of doing angular work; delta angular work/delta time; Watts