Mechanics & Simple Machines · AP Physics 1 Unit 3 (Circular Motion)
Uniform Circular Motion & Centripetal Force Simulator
Key exam takeaway: Centripetal force is not an independent physical force, but the net resultant force pointing toward the center of curvature.
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3D Simulation Stage● 60 FPS
Parameter Controls
m
m/s
kg
Live Derivations & Metrics
Centripetal Accel
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Centripetal Force
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Normal Force N
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Critical Velocity
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Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: A 1000kg car crosses a convex bridge (R=50m) at 10m/s. What is the normal force at apex? (g=10m/s²)
Step-by-Step Derivation:
- Apex equilibrium: mg - N = mv²/R => N = 1000*(10 - 100/50) = 8000N.
Worked Problem
Problem: A roller coaster loop has radius 10m. What is the minimum velocity at the top to prevent falling? (g=10m/s²)
Step-by-Step Derivation:
- At critical apex, N=0: mg = mv²/R => v_min = sqrt(gR) = sqrt(10*10) = 10m/s.
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: Is uniform circular motion truly uniform motion? Explain why.
Answer Key: No. While linear speed is constant, the direction of velocity changes continuously, requiring continuous inward acceleration.
Q2. Variant 2: Why are outer train rails banked on curves? What happens if speed exceeds design limit?
Answer Key: Banked tracks tilt normal force to provide centripetal force without wheel flange friction. Overspeeding forces wheel flanges against outer rail.
Q3. Variant 3: What physical principle enables washing machine spin dryers to extract water?
Answer Key: Centrifuge effect. As rotational speed increases, required centripetal force exceeds water-fabric adhesion, tossing droplets tangentially through drum holes.
Frequently Asked Questions & Misconceptions
Is "centrifugal force" a real physical force?
No! In an inertial frame, only centripetal force exists. Outward movement is due to inertia carrying the mass along the tangent when inward force is insufficient.
Does the net force do work in uniform circular motion?
Zero work! Centripetal force is strictly perpendicular to instantaneous displacement at all points, so W = F*s*cos(90°) = 0.
Why do brakes become ineffective if a car speeds over a convex bridge crest?
Higher speeds decrease normal force N, reducing maximum tire friction f=μN. At takeoff speed N=0, friction vanishes completely.
How many forces act on a conical pendulum bob?
Only two: gravity G and rope tension T. Centripetal force is their resultant vector (mg*tanθ). Never draw a separate centripetal force on the diagram!