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Contact: Eka Cahya Prima

"Tracker Analysis of Rolling Cylinders 101 by Eka Cahya Prima"

This document explores the motion of rolling cylinders using Tracker software, focusing on translational and rotational dynamics. The study aims to analyze how the physical properties of the cylinders, such as mass, radius, and moment of inertia, affect their motion on inclined planes or flat surfaces.

Study Guide:

Objective:

• Investigate the dynamics of rolling cylinders, examining the interplay between translational and rotational motion.
• Analyze energy distribution between kinetic and rotational components.

Key Concepts:

1. Rolling Motion:

   • A combination of translational motion of the cylinder’s center of mass and rotational motion about its axis.

2. Moment of Inertia (\( I \)):

   • A measure of an object’s resistance to rotational acceleration, dependent on its mass distribution.

3. Energy Conservation in Rolling:

   • Total energy is conserved and consists of translational kinetic energy (\( \frac{1}{2}mv^2 \)) and rotational kinetic energy (\( \frac{1}{2}I\omega^2 \)).

4. Rolling Without Slipping:

   • The condition \( v = r\omega \) ensures no relative motion between the cylinder and the surface.

Experiment Overview:

• Setup:
  Cylinders with varying masses and radii are rolled down an inclined plane. The motion is recorded and analyzed using Tracker software.

• Procedure:

  1. Place the cylinder at the top of an inclined plane and release it without applying force.
  2. Record the motion using a video camera.
  3. Import the video into Tracker to measure displacement, velocity, and angular velocity over time.
  4. Repeat the experiment with cylinders of different masses, radii, and materials.

• Observation Points:

  • Translational velocity of the center of mass.
  • Angular velocity of the cylinder.
  • Relationship between linear and rotational motion.

Questions to Consider:

1. What factors affect the acceleration of the rolling cylinder?

   • Answer: The incline angle, mass distribution (moment of inertia), and friction all influence acceleration.

2. How is energy distributed in rolling motion?

   • Answer: Energy is divided into translational and rotational kinetic energy. For rolling without slipping:

3. Why is the condition \( v = r\omega \) important?

   • Answer: This ensures that the cylinder rolls without slipping, maintaining a consistent relationship between linear and angular velocities.

4. How does the moment of inertia influence motion?

   • Answer: Cylinders with higher moments of inertia roll more slowly for the same incline, as more energy is stored in rotational motion.

5. What are the implications of varying the cylinder’s mass and radius?

   • Answer: These properties affect the moment of inertia and the cylinder’s ability to accelerate or maintain motion.

Applications:

• Physics Education: Demonstrating principles of energy conservation, rotational dynamics, and friction.
• Engineering Design: Understanding rolling motion in wheels and mechanical components.
• Material Science: Analyzing how material properties influence rolling behavior.

FAQ:

1. Why is rolling motion studied in this experiment?

   • Rolling motion illustrates the relationship between translational and rotational dynamics, providing foundational insights into mechanics.

2. What role does friction play in rolling?

   • Friction provides the torque needed for rotational motion and prevents slipping.

3. Can this experiment be expanded to other objects?

   • Yes, the principles apply to spheres, disks, and irregularly shaped objects, each with unique moments of inertia.

4. How does Tracker enhance the analysis?

   • Tracker allows precise measurements of displacement, velocity, and angular velocity, enabling detailed study of motion.

5. What challenges might arise in the analysis?

   • Factors like uneven surfaces, measurement errors, or insufficient friction may complicate data interpretation.

Research

http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4941183 Kinematics investigations of cylinders rolling down a ramp using tracker Eka Cahya Prima1,2,*, Menurseto Mawaddah1, Nanang Winarno1 andWiwin Sriwulan3