Lecture Notes: Rotational Motion

Key Topics Discussed:

• Rotational Equilibrium
• Center of Gravity
• Torque Calculation
• Practical Examples

1. Introduction to Rotational Equilibrium

• Rotational Dynamics Recap: Understanding rotational motion when objects can accelerate.
• Rotational Equilibrium:
  • Definition: A state where there is no acceleration, angular or otherwise.
  • Conditions: The sum of forces is zero and the sum of torques is zero.

2. Axis of Rotation

• Arbitrariness in Axis Choice:
  • The axis of rotation can be chosen for convenience rather than being physically fixed.
  • Example: Pivot points can be selected based on convenience for calculations rather than physical reality.

3. Torque and Equilibrium

• Example with Hockey Sticks:
  • Equal forces on both sides can cause rotational equilibrium.
  • Unequal application of torque results in non-equilibrium.

4. Gravitational Force and Center of Gravity

• Torque Due to Gravity:
  • The gravitational force acts on all parts of an object but is modeled at the center of gravity.
• Center of Gravity:
  • Acts as if all mass is concentrated there.
  • Balancing an object helps find its center of gravity.

5. Calculating the Center of Gravity

• Equations:
  • For point particles: Sum of (mass x position) / total mass.
  • Assumptions: Homogeneous objects considered to have centered mass.
  • Practicality: Geometrical center often used in theoretical calculations.

6. Practical Example: Seesaw Problem

• Scenario: Two children on a seesaw, calculating distances to balance.
• Steps:
  • Listed known values: masses, distances from pivot.
  • Developed an extended free body diagram.
  • Summed torques to find equilibrium conditions.
  • Calculated required position for child B to maintain balance.

7. Direction and Application of Forces

• Extended Free Body Diagram:
  • Importance of considering where forces are applied.
  • Not all forces produce torque; direction matters.
• Torque Calculation:
  • Important to consider angle of force application.
  • Forces do not always need to be perpendicular.

8. Recap and Conclusion

• Final Thoughts:
  • Example problems help understand rotational equilibrium.
  • Important to consider both magnitude and direction of forces.
• Action Items:
  • Complete the checkpoint.
  • Prepare questions for class discussion.

Note: The lecture highlights the significance of understanding rotational dynamics and equilibria, particularly in everyday scenarios like seesaws and balance boards. Practice solving problems by considering all forces and their applications.