Kabat Circular Motion Intro

Today's Schedule

  • Learning Objectives:

    1. Describe what is required to make an object move along a circular path.

    2. Define and calculate both centripetal force and centripetal acceleration.

    3. Analyze the motion of an object moving along horizontal circular paths.

  • To Do Today:

    1. Intro to circular motion

    2. Assignment: Circular Motion Practice

Circular Motion Basics

  • Circular motion involves objects moving along a circular path.

  • Key concepts include the forces acting on an object, acceleration, and the calculations involved.

Acceleration in Circular Motion

  • Question: A block of mass M is swung on a rope in a vertical circle with radius r at constant speed v. Is this object accelerating?

    • Answer: Yes, due to the change in direction which results in a change in velocity. Thus, the object is accelerating.

Historical Perspective

  • Earlier beliefs held that celestial bodies move in circular paths naturally.

  • The current understanding is that objects in motion tend to maintain constant velocity, and forces (such as gravity) act to change their direction.

Centripetal Force

  • To move in a circular path, a centripetal force is required, directed towards the center of the circle.

  • Centripetal means “center-seeking”.

Motion Dynamics

  • When an object moves in a circle, both acceleration and net force must point toward the center.

  • Formula: Summation of forces (ΣF) equals mass times acceleration (ma).

Understanding Centripetal Force

  • Centripetal force is not a standalone force; it can be provided by friction, tension, weight, etc.

  • Important Note: Do not label centripetal force (Fc) on free body diagrams (FBDs) as it isn’t an individual force.

Examples of Forces in Circular Motion

  1. Hamsters on a Circular Path:

    • Forces keeping hamsters in circular motion include friction and normal force from the wall.

    • Centripetal force is the sum of the friction and the normal force (Fc = f + FN).

  2. Cars Turning at Curves:

    • The force that enables a car to maintain circular motion is static friction.

    • Without friction, a car cannot turn (e.g., sliding on ice).

Forces Acting on Objects in Circular Motion

  • For cars or other vehicles rounding curves:

    • The static friction force acts toward the center of the circle.

  • Free Body Diagrams (FBDs):

    • Practicing drawing FBDs to understand force relationships during circular motion.

Centripetal Acceleration

  • Definition: Acceleration keeping an object in uniform circular motion.

  • Formula: [ a_c = \frac{v^2}{r} ]

    • Where:

      • ( a_c ): centripetal acceleration (m/s²)

      • ( v ): linear velocity (m/s)

      • ( r ): radius of the circle (m)

  • Centripetal acceleration points towards the center, while velocity is tangential to the circular path.

Application of Circular Motion Concepts

  1. Roller Coasters:

    • Analyze forces acting on riders at top and bottom of loops.

  2. Vehicle Dynamics:

    • Calculate maximum speed a vehicle can maintain circular motion based on mass and friction.

Assignments

  • Circular Motion Practice:

    • Engage with questions related to centripetal force and acceleration concepts.