Lecture 6C: Newton's Laws and Circular Motion

Key Concepts

• Newton's Laws in Circular Motion:

  • Newton's second law (F = ma) applies to circular motion due to the presence of acceleration.
  • Focus is on centripetal acceleration for uniform circular motion, not on tangential acceleration.

• Components of Forces:

  • Similar to straight line motion, forces in circular motion are analyzed in x and y components.
  • Use free body diagrams to isolate forces acting on a single object.

• No New Forces:

  • The same forces (weight, tension, normal force, friction) are considered in circular motion.

Types of Circular Motion

• Horizontal Circular Motion:

  • Analyzed through examples like a child on a merry-go-round.
  • Focus on static friction and centripetal force.

• Vertical Circular Motion:

  • Considers forces acting vertically, such as gravity and tension in a swinging ball.
  • Example problems illustrate differences at the top and bottom of the path.

Example Problems

1. Horizontal Motion Problems:

   • Example of a child on a merry-go-round assessing friction and period.
   • Calculation involves balancing forces and using centripetal acceleration.

2. Banked Curves:

   • Examines scenarios like cars on a banked highway curve.
   • Analyze forces using free body diagrams and identify centripetal force components.

3. Vertical Motion:

   • Discusses forces at top and bottom of vertical paths.
   • Focus on determining tension and apparent weight.

Concepts of Apparent Weight

• True vs Apparent Weight:

  • True weight is the gravitational force acting on a mass.
  • Apparent weight is what is felt due to normal or tension forces, especially in circular motion.

• Examples of Apparent Weight:

  • Person in free fall feels weightless due to lack of normal force.
  • In a rotating space habitat, apparent weight is felt because of centripetal acceleration.

Problem Solving Strategy

• Free Body Diagrams:

  • Essential for isolating forces acting on an object.
  • Helps visualize direction and magnitude of forces.

• Choosing Axes:

  • Align axes with direction of acceleration for simplicity in calculations.

• Evaluating Forces:

  • Consider all forces acting, using physics principles like Newton’s third law.

Summary

• Application of Newton's laws to circular motion involves the same fundamental principles as straight-line motion but adapted to include centripetal acceleration.
• Understanding apparent weight and its distinctions from true weight helps in analyzing circular motion problems.