Lecture Notes: Angular and Linear Kinematics

Introduction

• Discussing the relationship between angular kinematics (radius, angular velocity, angular acceleration) and linear kinematics (linear velocity, linear displacement).
• Introduce equations linking angular and linear displacement, velocity, and acceleration.

Angular vs. Linear Displacement

• Angular Displacement: Measures rotation (angle), e.g., the angle of a baseball bat swing.
• Linear Displacement: Distance covered by the tip of the bat.
• Relationship: Angle in radians = Arc length / Radius.

Angular and Linear Velocity

• Key Question: How to achieve maximal linear speed in sports?
• Application: Movements such as spiking or throwing in sports aim to maximize linear velocity.
• Relationship: Linear velocity (V) = Radius (R) * Angular velocity (ω).

Example

• Baseball Hitting: Different points on the bat result in different distances traveled by the ball.
• Equation: Increase in radius = Increase in arc length while angle remains constant.

Sports Application

• Extending joints (e.g., in pitching, spiking) maximizes speed.
• Illustration: Fully extending the arm increases radius, thus increasing arc length and eventually linear velocity.

Linear and Angular Acceleration

• Tangential Acceleration: Acts along the tangent to the rotational path, influencing speed.
• Radial (Centripetal) Acceleration: Directed inwards, maintaining the circular motion.

Equations and Calculations

• Tangential Acceleration: Radius * Angular acceleration.
• Radial Acceleration: V² / R or R * ω².
• Resultant Acceleration: Combines tangential and radial components.

Resultant Acceleration

• Overall linear acceleration of a rotating body.
• Equation: C² = A² + B², where C is the resultant acceleration.

Practical Examples

• Golf Swing: Linking angular acceleration to linear velocity.
• Baseball Pitch: Calculating net velocity from shoulder and elbow rotations.

Application in Sports Analysis

• Qualitative vs. Quantitative: Objective versus data-driven analysis.
• Usage in improving athlete performance by analyzing angular and linear kinematics.

Practice Problems

1. Convert degrees to radians.
2. Calculate relative angle from absolute angles.
3. Find segment's absolute angle via coordinates.
4. Determine angular velocity from initial and final angles over time.

Conclusion

• Strong emphasis on understanding the conversion between angular and linear systems.
• Reminder to attend future sessions for more practice and mastery of these concepts.