Overview
This lecture explains the concept of centripetal force, its sources, relevant formulas, and how to apply these ideas to solve physics problems involving circular motion.
Effects of Force Direction Relative to Velocity
- If force and velocity vectors are parallel, the object's speed increases.
- If force and velocity vectors are anti-parallel, the object's speed decreases.
- If force and velocity are perpendicular, the object turns at constant speed (uniform circular motion).
Centripetal Force and Its Sources
- Centripetal force keeps objects moving in circles and always points toward the center.
- Centripetal force is not a unique force; it's provided by tension (rope), gravity (planets), friction (cars), or magnetic force (charged particles).
- Examples:
- Rope tension for a ball on a string.
- Gravity for Earth orbiting the Sun.
- Static friction for a car turning.
- Magnetic force for a charged particle in a magnetic field.
Centripetal Force Formula and Dependencies
- Centripetal force: ( F_c = m \frac{v^2}{r} ).
- ( F_c ) increases with mass (( m )) and the square of speed (( v^2 )); decreases with larger radius (( r )).
- Doubling mass or speed changes ( F_c ) proportionally; doubling radius halves ( F_c ).
Sample Problems and Calculations
- Problem-solving steps: Identify knowns (mass, speed, radius), plug into ( F_c = m \frac{v^2}{r} ), solve for unknowns.
- Example calculations show changes to ( F_c ) when adjusting mass, speed, or radius.
- Formulas allow solving for missing variables (e.g., rearranging to solve for radius or speed).
Free Body Diagrams in Circular Motion
- Tension force in horizontal circles has horizontal (centripetal) and vertical (weight-balancing) components.
- If moving fast, tension is approximately equal to centripetal force.
- Exact tension: ( T = \sqrt{(m v^2 / r)^2 + (mg)^2} ).
Comparing Centripetal Force in Different Scenarios
- When speed changes and radius is constant: ( F_{c,2} = F_{c,1} \left(\frac{v_2}{v_1}\right)^2 ).
- When both speed and radius change: ( F_{c,2} = F_{c,1} \frac{r_1}{r_2} \left(\frac{v_2}{v_1}\right)^2 ).
Key Terms & Definitions
- Centripetal Force — Force that keeps an object moving in a circular path, pointing toward the center.
- Uniform Circular Motion — Motion in a circle at constant speed.
- Tension Force — Force transmitted by a rope or string.
- Static Friction — Friction that enables turning without slipping.
- Centripetal Acceleration — Acceleration toward the center: ( a_c = \frac{v^2}{r} ).
Action Items / Next Steps
- Practice solving problems using ( F_c = m v^2 / r ) for different scenarios.
- Review free body diagrams involving circular motion.
- Read ahead on magnetic force as a centripetal force (Physics 2 topic).