24.4 Newton's 2nd Law and Energy Conservation  Summary and Q&A
TL;DR
When solving physics problems involving circular motion, it is important to use both the energy principle and Newton's second law to account for forces in the radial and tangential directions.
Questions & Answers
Q: Why do we need to use both the energy principle and Newton's second law in circular motion problems?
Circular motion problems involve forces in both the radial and tangential directions. The energy principle only considers forces in the direction of motion, while Newton's second law in the radial direction accounts for forces perpendicular to motion. Both principles are necessary for a comprehensive analysis.
Q: Is the normal force included in the energy principle?
No, the normal force is not included in the energy principle because it is perpendicular to the displacement. The energy principle only considers the work done by the gravitational force in the direction of motion.
Q: How is the work done by gravitational force calculated in circular motion problems?
The work done by gravitational force in circular motion problems is the component of the force in the direction of motion, which is given by mg sine theta, multiplied by the displacement. This work accounts for the change in potential energy.
Q: What is the role of Newton's second law in circular motion problems?
Newton's second law is used to determine the forces in the radial and tangential directions. In circular motion, the radial direction equation is necessary to calculate the normal force, while the tangential direction equation is integrated to derive the energy principle.
Summary & Key Takeaways

Physics problems often involve fundamental principles such as Newton's second law and the energy principle.

Circular motion problems require the use of both Newton's second law in the radial direction and the tangentially integrated Newton's second law in the energy principle equation.

The energy principle only considers forces in the direction of motion, while Newton's second law in the radial direction accounts for forces perpendicular to motion.