Centripetal Force Calculator
Calculate centripetal force, acceleration, speed, radius, mass, frequency, and period with circular-motion visuals, unit conversions, and step-by-step explanations.
Background
Objects moving in a circle are constantly changing direction, so they need an inward net force. This calculator helps students connect the formula, the direction of acceleration, and real circular-motion situations.
How to use this calculator
- Choose the circular-motion mode that matches your problem.
- Select what you want to solve for: force, acceleration, mass, speed, radius, period, or frequency.
- Enter the known values with units, then click Calculate Centripetal Force.
- Use the visual to remember that velocity is tangent while force and acceleration point inward.
- Use quick examples to test common homework setups like flat curves, banked curves, and rpm problems.
How this calculator works
- For basic circular motion, it uses F = mv²/r and a = v²/r.
- It treats centripetal force as the inward net force, which may be provided by friction, tension, gravity, the normal force, or a combination of forces.
- For period or frequency problems, it first finds speed using v = 2πr/T or v = 2πrf.
- For flat curves, it compares required centripetal force with available static friction.
- For banked curves, it uses the ideal frictionless relationship tan θ = v²/(rg).
Formula & Equations Used
Centripetal force: F = ma = mv²/r
Centripetal acceleration: a = v²/r
Speed from period: v = 2πr/T
Speed from frequency: v = 2πrf
Flat curve friction limit: vmax = √(μsgr)
Ideal banked curve: tan θ = v²/(rg)
Example Problems & Step-by-Step Solutions
Example 1: Find centripetal force
A 2 kg object moves at 10 m/s in a circle with radius 5 m.
F = mv²/r
F = (2)(10²)/(5)
F = 40 N
The force points toward the center of the circle.
Example 2: Find speed from force
A 3 kg object needs 96 N of inward force to move in a circle of radius 12 m.
F = mv²/r
v = √(Fr/m)
v = √((96)(12)/3) = √384
v ≈ 19.6 m/s
Example 3: Check a flat curve
A 1200 kg car travels 15 m/s around a flat curve with radius 60 m and μs = 0.70.
Fc = mv²/r = (1200)(15²)/60 = 4500 N
Ffriction,max = μs mg = (0.70)(1200)(9.81) ≈ 8240 N
Because available static friction is greater than the required centripetal force, the curve is safe at this speed.
What centripetal force means
Centripetal force is not a new type of force. It is the inward net force required to keep an object moving in a circular path. Depending on the situation, that inward force may come from tension, friction, gravity, a normal force, or a combination of forces. On flat curves, friction often provides the inward force; on banked curves, the normal force can help provide it.
FAQ
What is centripetal force?
Centripetal force is the inward net force required to keep an object moving in a circular path. It is not a separate new force type; it can be provided by friction, gravity, tension, the normal force, or a combination of forces.
What formula does the Centripetal Force Calculator use?
The main formula is F = mv²/r. The calculator also uses a = v²/r, v = 2πr/T, v = 2πrf, vmax = √(μsgr) for flat-curve friction, and tan θ = v²/(rg) for ideal banked curves.
Is centripetal force inward or outward?
Centripetal force points inward, toward the center of the circle. The outward feeling in a turning car is not the centripetal force; the required net force for circular motion is inward.
Does mass affect centripetal acceleration?
No. Centripetal acceleration depends on speed and radius: a = v²/r. Mass affects how much force is needed to create that acceleration because F = ma.
What provides centripetal force in real examples?
For a car on a flat curve, static friction often provides the inward force. For a satellite, gravity provides it. For a ball on a string, tension provides it. For a roller coaster loop, gravity and the normal force can both contribute.
Can this calculator handle frequency, period, rpm, and banked curves?
Yes. The calculator can use period or frequency to find speed, convert rpm to Hz in frequency mode, compare flat-curve friction limits, and estimate ideal banked-curve speed or angle.
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