Angular kinematics

What is the definition of linear motion in biomechanics?

It is motion where all points on a body travel the same distance at the same time.

Definition of angular motion in biomechanics

It is motion where all points on a body rotate the same angular distance at the same time around an axis of rotation.

What key feature distinguishes angular motion from curvilinear motion?

Angular motion occurs around an axis of rotation, whereas curvilinear motion does not

What direction of rotation is typically considered positive (+)?

Counterclockwise (CCW) rotation is typically considered positive

What is the conversion factor between one radian and degrees?

1 radian = 57.3 degrees

Why are radians considered unitless or dimensionless?

Because a radian is a ration of two length (arc length divided by radius)

What is a segment or absolute angle?

The angle formed between a body segment and an imaginary external reference line.

What is the typical reference line used for calculating segment angles in biomechanics? 

The “right horizontal” which is a horizontal line extending to the right of the joint.

What is a joint or relative angle?

It is the angle formed between two adjacent body segments.

Provide the general formula used to calculate a segment angle (θsegment​) from coordinate data.

θsegment​=tan−1 y proximal​− y distal​ / x proximal​−x distal​​

What adjustment must be made to a calculated segment angle if the resulting coordinates (x,y) are in Quadrant 2 (-x, +y)?

add 180 degrees to the result of the inverse tangent calculation

What adjustment must be made to a calculated segment angle if the resulting coordinates (x,y) are in Quadrant 4 (+x, -y)?

add 360 degrees to the result of the inverse tangent calculation.

Why are adjustments needed when calculating segment angles that fall into Quadrants 2,3,or 4?

The adjustments ensure the final angle is correctly measured relative to the standard “right horizontal” reference line.

How is the knee joint angle (θkneejoint​) calculated using segment angles?

θkneejoint​=θthighsegment​−θlegsegment​

How is the hip joint angle (θhipjoint​) calculated using segment angles?

θhipjoint​=θthighsegment​−θtrunksegment​

How is the ankle joint angle (θanklejoint​) calculated using segment angles?

θ anklejoint​=θ legsegment​−θ footsegment​+90∘

Why is 90° added when calculating the ankle joint angle from segment angles?

To set the neutral position of the joint to 0°, aligning it with the anatomical position.

What motion does a positive (+) value for a calculated knee or hip joint angle typically represent ?

A positive value typically represents flexion

What motion does a negative (-) value for a calculated knee or hip joint angle typically represent?

A negative value typically represents extension.

What is the Q-angle?

It is a joint angle measured by extending a line from the ASIS to the center of the patella and another from the center of the patella to the tibial tuberosity.

According to recent research cited in the source material, what is the correlation between Q-angle and knee pain?

The research indicates there is no correlation between Q-angle and knee pain

Define angular displacement (Δθ) and provide its formula.

Angular displacement is the change in angular position, calculated as Δθ=θf​–θi

Angular displacement is frequently used in clinical settings to measure a joint’s

range of motion (ROM)

What are the common units of measure for angular velocity?

Degrees per second(0∘/sec) or radians per second (rad/sec).

Define angular acceleration (α) and provide its formula.

Angular acceleration is the rate of change of angular velocity, calculated as α=Δω​/=Δt

What is the key variable that serves as the link between linear and angular kinematics?

The radius of rotation ( r)

what unit must the angular displacement (θ) be in?

The angular displacement must be in radians

For any given point on a rotating body, the traveled depends on the length of the radius.

curvilinear distance (arc length)

For all points on a rigid rotating body, what kinematic quantity remains the same regardless of their distance from the axis of rotation?

The angular displacement (Δθ) is the same for all points

What is tangential velocity (VT)?

It is the linear velocity of a point on a rotating body, directed tangent to its circular path.

In sports like baseball or golf, tangential velocity is often referred to as               or             

bat speed; club head speed

What are the two variables that can be manipulated to increase tangential velocity (Vt)?

Increase the radius of rotation (r ) or increase the angular velocity (w)

How does a longer golf club, like a 3-iron, help generate more tangential velocity compared to a shorter 7-iron, assuming angular velocity is the same?

The longer club increases the radius of rotation (r), which directly increases the tangential velocity (vT​=rω).

What is centripetal acceleration( ar)?

It is center-seeking, inward acceleration that is necessary to keep an object moving along a curved path.

Why do track runners and speed skaters lean into a turn?

They lean into generate a horizontal ground reaction force, which provides the necessary centripetal acceleration to follow the curved path.

For a skater making a turn, the horizontal ground reaction force is directed towards the center of the track, causing,

centripetal acceleration

What biomechanical finding is associated with individuals who have had ACL reconstruction (ACLR)?

They often demonstrate decreased knee flexion angles and a reduced knee range of motion.

What is the biomechanical function of knee flexion during activities like landing?

Knee flexion is crucial for crucial absorption

A key difference between amateur and professional golfers is that professionals exhibit a higher peak angular velocity.

pelvis

What is the term for the curvilinear distance of a point of interest on a rotating segment?

Arc length (s)

If a golfer cannot change the length of their club (radius), how can they increase the club head’s tangential velocity?

By increasing their angular velocity (ω), meaning they must rotate faster.

Why can general human motion, like walking, not be described as purely linear or purely angular?

Because it involves both: the body's center of mass moves linearly (or curvilinearly) while the joints (hips, knees, ankles) undergo angular motion (flexion/extension).