3D Circular Motion Simulation

Circular Motion · Live

Speed8.0 m/sInward force32.0 NAcceleration16.0 m/s²Period1.57 sFᶜ = m × v² ÷ r

Orbits · Inward force · Tangent · Period

Circular-motion laboratory

Mission: change speed and watch the inward force grow rapidly while the object follows the same circle.

Real-world example

Moving mass2.0 kg

Orbit radius4.0 m

Tangential speed8.0 m/s

Simulation speed1×

Release object tangentially

Live measurements

Inward force32.0 N

Inward acceleration16.0 m/s²

Angular speed2.00 rad/s

Period3.14 s

Frequency0.32 Hz

DirectionTangent + inward

Equations with live values

aᶜ = v² ÷ raᶜ = 8.0² ÷ 4.00 = 16.0 m/s²

Fᶜ = m × aᶜ = m × v² ÷ rFᶜ = 2.0 × 16.0 = 32.0 N

ω = v ÷ rω = 8.0 ÷ 4.00 = 2.00 rad/s

T = 2 × π × r ÷ vT = 2 × 3.1416 × 4.00 ÷ 8.0 = 3.14 s

f = 1 ÷ T = v ÷ (2 × π × r)f = 1 ÷ 3.14 = 0.32 Hz

m = mass, v = tangential speed, r = radius, aᶜ = inward acceleration, Fᶜ = inward net force, ω = angular speed, T = period, f = frequency.

Force and acceleration graph

Force (N)Acceleration (m/s²)

Camera and focus

Focus: noneTap an object or arrow

Zoom1.0×

Tap the moving object, centre, path, inward-force arrow, or velocity arrow for a short explanation and compact close-up. Drag empty space to pan.

Teacher / Demo tools

Interactive visual lecture

The lecture begins only when you press Start. Every spoken relationship is animated, arrowed, or labelled on the canvas. A five-second prediction hook plays first.

Language

Narrator

Narration speed1×

Ready. Embedded offline audio is available.

Step 0 of 100%

Choose a chapter

What to watch: the orbit, arrows, and highlighted relationship.

Select a chapter or start the complete lecture.

Chapters

Learning objectives

Recognize that velocity is tangent to a circular path.
Identify inward acceleration and net force.
Predict how mass, speed, and radius change inward force.
Explain what happens when the inward force disappears.
Connect one model to roads, satellites, rides, and machines.

Core idea

An object moving in a circle is continually changing direction. That direction change requires an acceleration toward the centre. The required net inward force is Fᶜ = m × v² ÷ r. “Centripetal” describes the direction of the net force; it is not an extra new force.

Equation guide

aᶜ = v² ÷ r: inward acceleration increases with speed squared and decreases as radius grows.
Fᶜ = m × aᶜ: inward net force equals mass multiplied by inward acceleration.
ω = v ÷ r: angular speed tells how quickly the angle changes.
T = 2 × π × r ÷ v: period is the time for one complete revolution.
f = 1 ÷ T: frequency is the number of revolutions each second.

Suggested experiments

Double speed and compare the force before and after.
Double radius while keeping speed and mass fixed.
Increase mass and observe the proportional force change.
Release the object and inspect its tangent path.
Compare string tension, tire friction, gravity, and wall contact.

Explore and apply

Why do passengers feel pushed outward in a turning car? Why do roads use banked curves? How can gravity keep a satellite in orbit without pulling it straight down? Where does the inward force come from in a washing-machine drum?

Common misconceptions

The velocity does not point toward the centre; it points tangent to the path. An outward “centrifugal force” is not required in an inertial frame. A constant speed still involves acceleration because direction changes continuously.

Check your understanding

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