Chapter 11 Angular Kinematics of Human Movement (KNES 361)

How to Measure angles?

A goniometer is used to measure the angle between body segments

Joint angles are measured as segment of movement away from anatomical position 

The straight, fully extended position at a joint is regarded as zero degrees 

What is a body segment angle of orientation? 

Angular orientation of a body segment with respect to a fixed line of reference (usually horizontal or vertical) 

The angle of orientation of the trunk with respect to vertical is often the quantiles of interest in studies lifting as related to low back pain 

The angle of orientation of the trunk with respect to horizontal and angle of flexion is at the knee

What is angular displacement? 

• Change in angular position

• The directed angular distance from initial to final angular position

• The vector equivalent of angular distance 

• Measured in units of degrees, radians or rotations

EX: When the forearm returns to original position at the completion of a curl exercise, the angular displacement at the elbow is zero 

What is radian? 

The size of the angle subtended at the center of a circle by an arc equal in length to the radius of the circle

How is the direction of angular motion identified?

The direction of rotational motion is identified as positive (counterclockwise) or negative (clockwise)

What is angular velocity? 

The rate of change in angular position

Angular velocity = angular displacement / time (divided)

Measured in units of degrees / s (divide) or radians / s (divide)

What are the Relationships Between Linear and Angular displacement?

The greater the radius between a given point on a rotating body and the axis of rotation, the greater the linear displacement traveled by that point during an angular motion

The larger the radius of rotation (r) the greater the linear distance (s) traveled by a point on a rotating body 

s=r circle slashed

EX: A rotating stick simultaneously strikes 3 balls demonstrates the significance of the radius of rotation

What is the relationship between linear and angular velocity?

Since velocity is displacement over time, linear and angular velocity are related by the same factor that relates displacement: the radius of rotation (r)

v= r small person

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

What is angular acceleration?

• The rate of change in angular velocity

• Angular acceleration ang. velocity / time (divide)

• Measured in units of deg / s² or rad / s²

What is the relationship between linear and angular acceleration?

The acceleration of a body in angular motion can be resolved into two perpendicular linear accelerations components

What is tangential acceleration?

• Component of acceleration of angular motion directed along a tangent to the path of motion

• Represents change in linear speed

• at = v2-v1 / t

What is radial acceleration?

• Component of acceleration of angular motion directed towards the center of curvature

• Represents change in direction 

• ar= v² / r

What is total acceleration at release?

Because tangential and radial accelerations are perpendicular to one another, you can use Pythagorean theorem to solve for total acceleration

What is the relationship between units of measure of linear and angular motion?