10.472
m/s
2.0944
rad/s
0.3333
Hz
21.9325
m/s²
43.8649
N
31.4159
m
20
rpm
10.472
m/s
2.0944
rad/s
0.3333
Hz
21.9325
m/s²
43.8649
N
31.4159
m
20
rpm
The Circular Motion Calculator computes the key quantities of uniform circular motion from three fundamental inputs: mass, radius, and period. When an object travels in a circle at constant speed, it continuously changes direction, which means it is always accelerating. This centripetal acceleration points toward the center of the circle and requires a net inward force — the centripetal force.
Circular motion appears everywhere in physics and engineering: satellites orbiting Earth, cars navigating curves, electrons spiraling in magnetic fields, and centrifuges separating biological samples. The mathematical framework connecting period, velocity, acceleration, and force provides the foundation for analyzing all these systems. Our calculator instantly determines tangential velocity (v = 2πr/T), angular velocity (ω = 2π/T), centripetal acceleration (a_c = v²/r), centripetal force (F_c = mv²/r), and frequency (f = 1/T).
Whether you are a physics student solving homework problems, an engineer designing rotating machinery, or a scientist analyzing orbital mechanics, this tool gives you immediate, accurate results for uniform circular motion.
The calculator applies the standard equations of uniform circular motion:
Tangential velocity: $$v = \frac{2\pi r}{T}$$ — the linear speed along the circular path.
Angular velocity: $$\omega = \frac{2\pi}{T}$$ — how fast the angle changes in radians per second.
Centripetal acceleration: $$a_c = \frac{v^2}{r} = \omega^2 r$$ — always directed toward the center.
Centripetal force: $$F_c = ma_c = \frac{mv^2}{r}$$ — the net inward force required to maintain circular motion.
Frequency: $$f = \frac{1}{T}$$ — revolutions per second (Hz). Enter the mass of the object, the radius of the circular path, and the period (time for one full revolution).
The centripetal acceleration tells you how many g-forces the object experiences (divide a_c by 9.81). Fighter pilots experience ~9g in tight turns; amusement park rides typically stay below 4g. The centripetal force is not a new force — it is the net inward force provided by tension, gravity, friction, or normal force depending on the situation. If the required centripetal force exceeds the available force (e.g., tire friction on a curve), the object will fly off tangentially.
Inputs
Results
A 0.5 kg ball swung in a 1.2 m radius circle with a 1.5 s period requires about 10.5 N of tension in the string — more than twice the ball's weight.
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Results
A 1500 kg car on a 50 m radius curve at ~26 m/s (94 km/h) needs over 20.5 kN of friction force, about 1.4g of lateral acceleration.
Centripetal force is the real net inward force that keeps an object moving in a circle (friction, tension, gravity). Centrifugal force is a fictitious (pseudo) force that appears only in a rotating reference frame, directed outward. In an inertial frame, only centripetal force exists.
Gravity provides the centripetal force. The gravitational pull of Earth continuously deflects the satellite's straight-line trajectory into a curved orbit. Setting F_gravity = F_centripetal gives the orbital velocity equation.
Use T = 2πr/v. For example, if v = 10 m/s and r = 5 m, then T = 2π(5)/10 = 3.14 seconds per revolution.
As speed increases, the object covers more arc per unit time and must change direction more rapidly. The rate of change of the velocity vector scales with v², giving a_c = v²/r.
No. Uniform circular motion always requires a net inward (centripetal) force. If the net force is zero, the object moves in a straight line at constant velocity (Newton's first law). Any deviation from straight-line motion requires a force.
The object flies off in a straight line tangent to the circle at the point of release (Newton's first law). This is the principle behind hammer throwing in athletics and slingshot maneuvers in space.
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The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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