Angular kinematics

Question 1

What is angular motion?

Answer 1

Angular motion- the movement that occurs about a fixed axis of rotation. It occurs when a force is applied outside of the axis of rotation.

Rotation about a point of contact (floor, bar)

Rotation about the centre of mass (aerial activities)

Rotation about joint centres is fundamentally how we move and causes general motion (a combination of linear and angular motion). Describing angular motion can have important implications for performance and injury.

3 planes of motion- 3 ways to move linear across a plane (translation)

3 axis of rotation- 3 ways to rotate about an axis perpendicular to a plane (rotation)

Question 2

What is an angle and a radian?

Answer 2

An angle is comprised of 2 intersecting lines at a point (vertex). The lines are usually body segments; the vertex is a joint. SI units for angles is radians; degrees are commonly used.

1 radian= the angular distance covered when the arc length equals the radius.

Theta = arc length / radius = 1 rad

Circumference/Radius = (2pi x r)/r = 2pi

180 degrees = pi rad

Question 3

What is an absolute (segment) angle?

Answer 3

Absolute (segment) angle- the angle of inclination of a line (segment) relative to a fixed reference. Describes the orientation of a line in space. Fixed reference = right horizontal. Reference is normally taken from the distal point of the body segment. Anti-clockwise rotation = positive rotation.

Theta = inverse tan( y proximal-y distal / x proximal-x distal)

Question 4

What is the relative (joint) angle?

Answer 4

Relative (joint) angle- the angle between 2 lines that describes the configuration of 2 segments without defining the orientation of the segments in space. Used to calculate the angle at a joint. Flexion is defined as negative, extension as positive.

Question 5

What is the cosine rule and segment absolute angle equations?

Answer 5

cos = (b^2 + c^2 -a^2) / 2bc
0= full flexion, 180= full extension

theta knee (angle at the knee) = 180 - (max angle - min angle)

Question 6

What is angular displacement?

Answer 6

Angular displacement- the change in orientation of a segment/joint position (change in absolute or relative angle). Referred to as ‘range of motion’ (ROM).

Angular displacement= final angle – initial angle

Anti-clockwise rotation = positive displacement
Clockwise rotation = negative displacement
Flexion ROM = negative displacement
Extension ROM = positive displacement

Question 7

What is angular velocity?

Answer 7

Angular velocity- the rate of change in angular displacement/ slope of the angle-time curve

Angular velocity = (final angle – initial angle) / change in t

Anti-clockwise rotation = positive angular velocity
Clockwise rotation = negative angular velocity
Flexion ROM = negative angular velocity
Extension ROM = positive angular velocity

Question 8

What is angular acceleration?

Answer 8

Angular acceleration- the rate of change in angular velocity/slop of the angular velocity-time curve. Has the angular velocity increased or decreased over a period of time.

Angular acceleration = (Final angular velocity – Initial angular velocity) / change in t

Question 9

What is curvilinear distance and tangential velocity?

Answer 9

The greater the radius, the greater the curvilinear distance (arc length) travelled by the distal end of the object.

Curvilinear distance (l) = radius x angle in radians

The greater the radius, the greater the linear velocity for a given angular velocity.

Tangential velocity = velocity perpendicular to the rotating object

Tangential velocity (VT) = r x w (angular velocity)

Angular motion is used to increase the linear velocity of an implement (hammer throwing, golf swing, baseball). Increasing the angular velocity of a golf club and the radius rotation (club and arm), increases the ball’s velocity at impact.

Question 10

What is tangential acceleration and centripedal acceleration?

Answer 10

The greater the radius, the greater the linear acceleration for a given angular acceleration.

Tangential acceleration = acceleration perpendicular to the rotating object

Tangential acceleration (ar) = r x a

ar = (VTf – VTi) x change in t

Centripetal/radial acceleration describes the acceleration towards the axis of rotation (centre-seeking).

Centripetal acceleration (ac) = inward acceleration to the axis of rotation

ac = r x w^2

ac = VT^2 / r