Circular Motion Simulator

An object moving in a circle is always accelerating — toward the center — even at constant speed. That center-seeking acceleration needs a center-seeking force, the centripetal force. Spin the mass in this simulator and feel how radius, speed and mass each change the force the string must provide.

Radius 90 px

Speed 60 px/s

Mass 2 kg

Centripetal accel 40.0 px/s²Centripetal force 80.0 NPeriod 9.42 s

Controls

Radius: Length of the string in meters — how big the circle is.
Speed: The tangential speed of the mass in m/s. Direction changes constantly; magnitude stays fixed.
Mass: Mass of the spinning object in kg.

The physics

a_c = \frac{v^2}{r}

Centripetal acceleration, always toward the center

F_c = \frac{mv^2}{r}

Centripetal force required to hold the circular path

T = \frac{2\pi r}{v}

Period — time for one full revolution

Assumptions

Uniform circular motion (constant speed)
The string is massless and inextensible
Motion is in a horizontal plane — gravity is balanced by the support
No air resistance

Guided activity

Fix radius at 1.0 m and mass at 1.0 kg. Set speed to 2 m/s, record the force. Now double the speed to 4 m/s — what happens to the force?
Reset to speed 2 m/s. Double the radius to 2.0 m. Does the force double, halve, or stay the same?
Now double the mass instead. How does the force respond compared to doubling the speed?
Set r = 0.5 m and v = 3 m/s. Use the period equation to predict the time per revolution, then time the animation.

Challenge questions

Doubling the speed quadruples the force, but doubling the radius only halves it. Explain why speed is 'more powerful' using the v²/r structure.
A car turning a corner relies on friction for its centripetal force. What happens if the required mv²/r exceeds the maximum static friction?
The Moon orbits Earth once per ~27.3 days at ~384,000 km. Estimate its centripetal acceleration and identify the force providing it.