AP Physics 1 Unit Plan-Circular Motion and Gravitation

Unit Title: Circular Motion and Gravitation

Course: AP Physics 1
Duration: 2 weeks

Unit Objectives:

By the end of this unit, students should be able to:

1. Understand and apply the concepts of uniform circular motion.
2. Analyze forces acting on objects in circular motion.
3. Derive and use equations for centripetal acceleration and force.
4. Understand Newton's Law of Universal Gravitation.
5. Solve problems involving orbital motion and gravitational forces.

Key Topics:

6. Uniform Circular Motion

   • Centripetal acceleration: $a_c=\frac{v^2}{r}$
   • Centripetal force: $F_c=\frac{m{v}^2}{r}$
   • Relationship between linear velocity, angular velocity, and radius: $v=r\omega$

7. Forces in Circular Motion

   • Tension, friction, and normal forces in circular motion scenarios.
   • Free-body diagrams for circular motion.

8. Newton's Law of Universal Gravitation

   • Gravitational force: $F_g=G\frac{m_1{m}_2}{r^2}$
   • Gravitational field strength: $g=\frac{F_g}{m}=\frac{GM}{r^2}$

9. Orbital Motion

   • Orbital velocity: $v=\sqrt{\frac{GM}{r}}$
   • Period of orbit: $T=2\pi \sqrt{\frac{r^3}{GM}}$
   • Kepler's Laws (qualitative understanding).

Lesson Breakdown:

Week 1: Uniform Circular Motion

• Lesson 1: Introduction to circular motion

  • Define uniform circular motion.
  • Derive centripetal acceleration formula.
  • Practice problems on $a_c=\frac{v^2}{r}$.

• Lesson 2: Centripetal Force

  • Explore forces causing circular motion (tension, friction, gravity).
  • Free-body diagrams for circular motion.
  • Practice problems on $F_c=\frac{m{v}^2}{r}$.

• Lesson 3: Applications of Circular Motion

  • Vertical circular motion (e.g., roller coasters, pendulums).
  • Banked curves and frictionless motion.

Week 2: Gravitation

• Lesson 4: Newton's Law of Universal Gravitation

  • Derive and discuss $F_g=G\frac{m_1{m}_2}{r^2}$.
  • Gravitational field strength: $g=\frac{GM}{r^2}$.
  • Practice problems on gravitational forces.

• Lesson 5: Orbital Motion

  • Derive orbital velocity: $v=\sqrt{\frac{GM}{r}}$.
  • Discuss period of orbit: $T=2\pi \sqrt{\frac{r^3}{GM}}$.
  • Practice problems on satellites and planets.

• Lesson 6: Kepler's Laws (Qualitative)

  • Overview of Kepler's three laws of planetary motion.
  • Relate Kepler's laws to Newtonian mechanics.

Student handout: Student Handout-AP Physics 1-Circular Motion and Gravitation