Biomechanics lecture 5b

relative angle

formed between longitudinal axes of two adjacent body segments articulating at a joint, for example the lead knee when sprinting

absolute angle

angular orientation of a single body segment with respect to a fixed line of reference, for example the trunk with respect to vertical (back pain)

angular displacement

change in angular position from initial to final angular position, vector equivalent of angular distance, measured in units of degrees, radians, or rotations

what is a 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

90 degrees is equal to

1/2 pi radians

180 degrees is equal to

pi radians

270 degrees is equal to

3pi/2 radians

360 degrees is equal to

2pi radians (1 revolution)

angular displacement is positive when motion is

counterclockwise

angular displacement is negative when motion is

clockwise

the angle theta is defined to be

the arc length (s) divided by the radius (r)

1 radian is equal to 360/2pi which equals

57.3 (the conversion)

angular velocity

rate of change in angular position measured in degrees per second or radians per second

what is the relationship 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 distance traveled by that point during an angular motion

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

formula relating linear and angular MOTION

s (arc length) = r(theta/angle)

formula that related linear and angular VELOCITY

V (velocity) = rw (omega[angular velocity])

angular acceleration

rate of change in angular velocity, measured in units of degrees per second squared or radians per second squared, alpha

what is the relationship between linear and angular ACCELERATION

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

What is tangential acceleration

a sub t, component of acceleration of angular motion directed along a tangent to a path of motion. Represents change in linear speed

tangential acceleration equation

a sub t = ((v2 - v1)/t)r

what is radial acceleration?

a sub r. Component of acceleration of angular motion directed toward the center of curvature. Represents change in direction.

radial acceleration equation

a sub r= v^2/r

ANOTHER equation for tangential acceleration

a sub t = angular acceleration (alpha/a) x r