Calculate centripetal acceleration, force, angular velocity, period, bank angle, and g-force for uniform circular motion. Covers cars, coasters, satellites, centrifuges.
The **Circular Motion Calculator** analyses uniform circular motion — any object moving in a circle at constant speed. Enter mass, speed, and radius, and the calculator returns centripetal acceleration, centripetal force, angular velocity, period, frequency, RPM, g-force, ideal bank angle, minimum friction coefficient, and angular momentum. That makes it useful for both classroom physics and quick engineering checks. It also helps you compare how the same setup behaves when speed or radius changes.
Uniform circular motion underlies countless systems: cars negotiating curves, roller coasters in loops, satellites orbiting Earth, planets orbiting stars, centrifuges separating blood samples, and electrons spiralling in magnetic fields. Newton's second law applied in the radial direction gives F = mv²/r — the force required to maintain the circular path.
Explore presets for highway curves, roller coasters, LEO satellites, centrifuges, velodromes, and F1 racing, and use the speed-force table to see how centripetal demand changes with velocity. The grouped outputs make it easier to connect the same motion to both force-balance questions and comfort or safety limits in the real system.
Use this calculator to move from speed and radius to force, acceleration, g-load, bank angle, and period when checking turns, loops, orbiting bodies, or rotating equipment. It gives you the main circular-motion quantities together so you can judge whether a setup is physically reasonable. That is especially helpful when you want a quick check before a more detailed dynamics analysis. It also helps reveal how quickly the load climbs when speed increases.
Centripetal Acceleration: ac = v²/r Centripetal Force: Fc = m × ac = mv²/r Angular Velocity: ω = v/r Period: T = 2π/ω Frequency: f = 1/T Bank Angle (no friction): θ = arctan(v²/(rg)) Minimum Friction (flat): µ = v²/(rg)
Result: ac = 3.13 m/s² (0.32 g), Fc = 4 688 N, T = 50.3 s
A 1 500 kg car taking a 200 m radius highway curve at 90 km/h (25 m/s) needs 4 688 N of centripetal force — provided by tyre friction (µ ≈ 0.32).
Centripetal demand scales with the square of speed and inversely with radius. That means small changes in speed often matter more than people expect. Double the speed and the required inward force becomes four times larger.
In transport and ride design, the most practical outputs are usually g-load, required friction, and ideal bank angle. Those values tell you whether a curve is comfortable, whether a flat surface can hold the motion without slipping, and how much geometry can replace friction.
The so-called centrifugal force is a frame-dependent effect, not an extra physical force acting in an inertial frame. For force-balance work, always identify the real inward force source first, whether it comes from gravity, tension, friction, or the normal reaction.
The net inward force required to keep an object moving in a circle. It is not a separate force — it is provided by tension, gravity, friction, or normal force, depending on the situation.
Centrifugal force is a fictitious (pseudo) force that appears in the rotating reference frame. In an inertial frame, only centripetal (inward) force exists, so the outward pull is just a frame effect.
On a flat road, the only horizontal force is friction. Without enough friction (µ < v²/rg), the car slides outward, so tyre grip sets the safe speed.
A banked turn tilts the normal force inward, reducing or eliminating the need for friction. At the ideal bank angle, friction is zero and the road geometry supplies the centripetal force.
Sustained 5–6 g causes loss of consciousness (G-LOC). Fighter pilots with g-suits tolerate 9 g briefly, while roller coasters stay below 5 g for comfort and safety.
By spinning samples at high RPM, centrifuges create thousands of g, forcing denser particles outward. Medical centrifuges run at 3 000–15 000 RPM depending on the separation required.