Biomechanics Midterm 2 (theory)

Kinematics – The Study of Motion (Kinematics)

The study of motion without considering the forces that cause it.

Kinematic Variables

Time, position, displacement, velocity, acceleration (and rotational equivalents).

Descriptive

Descriptive kinematics quantifies movement (what happened), while explanatory kinematics seeks to explain why it happened.

Explanatory Kinematics Explanatory Kinematics

Qualitative Kinematic Analysis

A non-measured approach used by coaches and clinicians. Fast but lacks precise comparisons.

Quantitative Kinematic Analysis

Uses specialized equipment to provide objective, measurable data for research and clinical applications.

Rectilinear Translation

All points of a body move in a straight line at the same speed.

Curvilinear Translation

All points of a body follow curved but parallel paths.

Rotational (Angular) Motion

All points rotate around a fixed axis, moving through the same angle in the same time.

General Planar Motion

A combination of translation and rotation in a single plane.

Distance

The total length of the path traveled by a body (scalar quantity).

Displacement

The straight-line change in position from the initial to the final point (vector quantity, with magnitude and direction).

Speed

The rate of change of distance over time (scalar, m/s).

Velocity

The rate of change of displacement over time (vector, m/s).

Instantaneous Velocity

The velocity of an object at a specific moment in time.

Average Velocity

The total displacement divided by total time. If the start and end positions are the same, average velocity is zero.

Acceleration

The rate of change of velocity over time.

Positive Acceleration

Occurs when velocity increases in the positive direction or decreases in the negative direction.

Negative Acceleration

Occurs when velocity decreases in the positive direction or increases in the negative direction.

Constant Acceleration

When the acceleration remains the same over time, motion equations can be applied.

Projectile

A body in the air subject only to gravity and air resistance.

Three Factors Affecting Projectile Motion

• Projection Angle

• Projection Velocity

• Projection Height

Projection Angle

Influences trajectory shape. Maximum range occurs at 45° (without air resistance).

Projection Velocity

Higher initial velocity increases range and flight time.

Projection Height

A higher release point increases flight time and range.

Effect of Projection Angle

For equal initial velocities:

• Higher angles (90°)

• (below 45°)

Higher angles (90°)

Greater height, less range. Lower angles

Horizontal angles (below 45°)

Greater range if projection height is above landing height.

Horizontal of a Projectile

No acceleration (constant velocity).

Vertical Motion of a Projectile

Affected by gravity (-9.81 m/s²).

Trade-off Between Factors

The same height or range can be achieved with different combinations of velocity, angle, and height.

Angular Kinematics

The Study of Rotational Motion

Angular Motion

All points in an object move along circular paths around an axis.

Angular Kinematics

The study of motion in terms of angular displacement, velocity, and acceleration.

Angular vs. Linear Motion

Angular kinematics is similar to linear kinematics but describes rotational movement.

Angular Displacement (Definition)

The change in angular position, measured in radians (rad).

Radians and Degrees

1 rad = 57.3°, π rad = 180°.

Positive Angles

Counterclockwise rotation.

Negative Angles

Clockwise rotation.

Angular Displacement is Not a Vector

Because it does not follow vector addition rules.

Angular Velocity (ω)

The rate of change of angular displacement over time.

Angular Acceleration (α)

The rate of change of angular velocity over time.

Average Angular Velocity

ω = Δθ / Δt.

Average Angular Acceleration

α = Δω / Δt.

Constant Angular Acceleration

If α is constant, motion equations for constant acceleration apply to rotational motion.

Absolute Segment Angle

The angular position of a segment relative to a fixed reference (e.g., a horizontal line).

Relative Joint Angle

The angle between two adjacent body segments.

Computing Angular Displacement

Found by subtracting final and initial angular positions.

Curvilinear Displacement (Arc Length)

s = rθ,

• where s = arc length, r = radius, and θ = angular displacement.

Linear Velocity in Rotational Motion

v = rω

• v = linear velocity, r = radius, and ω = angular velocity.

Effect of Increasing Radius

Larger radius (r) → Greater linear displacement (s) and velocity (v) for a given angular displacement and velocity.

Tangential (Transverse) Velocity

Linear velocity is always tangent to the circular path.

Radial Axis

Extends outward from the center of rotation.

Transverse Axis

Perpendicular to the radial axis.

Transverse Acceleration (at)

Occurs when angular velocity changes (at = rα).

Radial (Centripetal) Acceleration (ar)

Occurs in any circular motion, keeping the object moving along a curved path.

Radial Acceleration Formula

• ar = rω²

• ar = v²/r.

Total Linear Acceleration

The sum of radial and transverse acceleration components.

Radial Acceleration in Sports (Sprinting on a Curve)

Tighter turns require greater radial acceleration, meaning inside lanes require more force to stay on track.

Baseball Bat Swing

A longer bat radius results in higher bat speed at the contact point.