#AP Physics 1: Free Body Diagrams & Circular Motion - The Ultimate Study Guide 🎢

Hey there, future AP Physics master! Let's break down Free Body Diagrams (FBDs) and circular motion. This guide is designed to be your go-to resource the night before the exam. Let's get started!

#1. Free Body Diagrams (FBDs) Basics 🎯

#What's an FBD?

• A free body diagram (FBD) is a visual tool that shows all the forces acting on an object. It helps us analyze motion, especially in scenarios like uniform circular motion. Think of it as a force map! 🗺️

#How to Draw FBDs

• Method 1 (Point Mass): Represent the object as a dot and draw arrows outward from the dot to represent forces. This is what we'll use in this guide.
• Method 2 (Detailed): Draw forces at the specific points where they are exerted on the object. Useful for more complex analysis.

#Coordinate System

• Always choose a coordinate system where the positive x or y axis points towards the center of the circle. This simplifies your analysis of centripetal force. 💡

#2. FBDs for Uniform Circular Motion 🔄

#Key Idea

• In uniform circular motion, the net force (centripetal force) always points towards the center of the circle. This force is what causes the object to move in a circular path.

#Gravity and Centripetal Force

• The gravitational force doesn't always point downwards. For example, in a planet's orbit, gravity acts as the centripetal force, pointing toward the center of the orbit (e.g., the sun). 🪐

#Other Forces

• Consider all forces: contact forces like tension, friction, and normal force, and non-contact forces like gravity. Don't forget any! 🧐

#3. Roller Coaster FBDs: A Case Study 🎢

Let's analyze a roller coaster at different points in a loop-the-loop. Remember, in uniform circular motion, the tangential velocity is constant, so there's only centripetal acceleration, no tangential acceleration.

#Roller Coaster Positions

• Red: Top of the loop
• Orange: Right side of the loop
• Green: Left side of the loop
• Yellow: Bottom of the loop

#Top of the Loop (Red)

• Both normal force (Fn) and gravity (Fg) point downwards (towards the center of the circle).

• Net force equation: Fnet = Fn + Fg

#Bottom of the Loop (Yellow)

• Normal force (Fn) points upwards (towards the center), gravity (Fg) points downwards.

• Normal force is greater than gravity to provide the centripetal force.

• Net force equation: Fnet = Fn - Fg

#Sides of the Loop (Orange and Green)

• Normal force (Fn) points towards the center of the circle (left for green, right for orange), gravity (Fg) points downwards.

• Net force equation: Fnet = Fn (since Fn is the only force contributing to centripetal acceleration)

Understanding the relationship between normal force and apparent weight is crucial for circular motion problems. Remember, apparent weight is how heavy you feel.

#4. Final Exam Focus 🎯

#High-Priority Topics

• Free Body Diagrams: Master drawing and interpreting them.
• Centripetal Force: Understand its direction and role in circular motion.
• Normal Force: Know how it changes in different scenarios.
• Apparent Weight: Grasp how it relates to normal force.

#Common Question Types

• Multiple Choice: Conceptual questions about forces in circular motion.
• Free Response: Drawing FBDs, calculating net force, and applying Newton's Second Law.

#Last-Minute Tips

• Time Management: Don't spend too long on one question. Move on and come back if needed.

• Common Pitfalls: Watch out for incorrect force directions and forgetting forces.

• Strategies: Draw clear FBDs, write down your equations, and show your work.

#5. Practice Questions

Practice Question

#Multiple Choice Questions

1. A car is moving at a constant speed around a horizontal circular track. What is the direction of the net force on the car? (A) Tangent to the circle (B) Radially inward (C) Radially outward (D) Zero

2. A ball is swung in a vertical circle at a constant speed. At which point in the circle is the tension in the string the greatest? (A) At the top of the circle (B) At the bottom of the circle (C) At the sides of the circle (D) The tension is the same at all points

3. A satellite is orbiting Earth in a circular path. If the mass of the satellite were doubled, what would happen to the centripetal force required to maintain the same orbit? (A) It would be halved (B) It would remain the same (C) It would be doubled (D) It would be quadrupled

#Free Response Question

A 2.0 kg block is placed on a frictionless, horizontal surface. The block is attached to a string that passes through a hole in the center of the surface. The block is spun in a circle with a radius of 0.50 m at a constant speed of 3.0 m/s. The string is held from below the surface.

(a) Draw a free body diagram of the block, labeling all forces acting on it.

(b) What is the centripetal acceleration of the block?

(c) What is the tension in the string?

(d) If the speed of the block is doubled, what will be the new tension in the string?

Scoring Breakdown

(a) (3 points) - 1 point for correct FBD (Tension towards the center, Normal force upwards, Gravity downwards) - 1 point for correct labeling of tension - 1 point for correct labeling of normal force and gravity

(b) (2 points) - 1 point for using the correct formula for centripetal acceleration: $a_c = v^2/r$ - 1 point for correct calculation: $a_c = (3.0 m/s)^2/0.50 m = 18 m/s^2$

(c) (2 points) - 1 point for using Newton's second law: $F_{net} = ma_c$ - 1 point for correct calculation: $T = (2.0 kg)(18 m/s^2) = 36 N$

(d) (3 points) - 1 point for recognizing that doubling the speed will quadruple the centripetal acceleration - 1 point for correct calculation of new acceleration: $a_c = (6.0 m/s)^2/0.50 m = 72 m/s^2$ - 1 point for correct calculation of new tension: $T = (2.0 kg)(72 m/s^2) = 144 N$