Chapter 11: Angular Kinematics of Human Movements

What is a relative angle?

the joint angle formed between two body segments

Compare the relative angle of the knee during sprinting vs distance running.

The relative angle at the knee tends to be smaller during sprinting than during distance running

What is an absolute angle?

• the angular orientation of a body segment with respect to a fixed line of reference

• reference lines are usually vertical or horizontal

Give an example of an absolute angle.

• the angle of the thigh with respect to the vertical during a squat

• the angle of one’s back with the wall when they go to pick something up

____ is the change in angular position

angular displacement

Angular Displacement

the angular distance from starting to finishing point

Angular displacement is the vector equivalent to _______.

angular distance

What are the units angular displacement is measured in?

degrees, radians, or rotations

Radian

the size of the angle formed at the center of the circle when the arc length is equal to the radius of the circle

What is 90 degrees in radians and revolutions?

• π/2 radians

• ¼ revolution

What is 180 degrees in radians and revolutions?

• π radians

• ½ revolution

What is 270 degrees in radians and revolutions?

• 3π/2 radians

• ¾ revolutions

What is 360 degrees in radians and revolutions?

• 2π radians

• 1 revolution

Angular Velocity

the change in angular position over time

Angular velocity equation:

Angular velocity (ω) = angular displacement (θ) / time (t)

What units are angular velocity measured in?

• degrees / s

• radians / s

Angular Acceleration

the rate of change in angular velocity

Angular Acceleration equation

Angular acceleration (α) = change in angular velocity (Δω) / time (t)

What units are angular acceleration measured in?

• degrees / s²

• radians / s²

What is the relationship between linear and angular displacement?

• the greater the radius of rotation ®, the greater the linear distance (s) traveled by a point on a rotating body

• s = rΦ

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 ®

• v = rω

What is the relationship between linear and angular acceleration?

the acceleration of a body in angular motion can be broken down into two perpendicular linear acceleration vectors

Tangential acceleration

the part of angular acceleration that acts along the tangent to the circular path, causing a change in speed

What does tangent mean?

tangent is a line that touches the circle and points in the direction the object is moving at that instant

Tangential acceleration represents what?

a change in linear speed

Equation for tangential acceleration:

at = (v2 -v1) / t

Radial acceleration

the vector of angular acceleration that is directed toward the center of curvature

Equation for radial acceleration:

Angular acceleration (ar) = ω² t