Calculate centripetal force from mass, radius, and either speed, RPM, or period, with unit conversions for kg, m/s, rev/min, and time.
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Angular (Centripetal) Force Formula
The calculator finds centripetal force, which is the inward force needed to keep a mass moving in a circular path. It converts your inputs to SI units first, then applies the formula for the mode you select.
Using linear speed
F_c = \frac{m v^2}{r}- Fc = centripetal force, in newtons (N)
- m = mass, in kilograms (kg)
- v = linear velocity, in meters per second (m/s)
- r = radius of the circular path, in meters (m)
Using RPM
F_c = m\omega^2r
\omega = \frac{2\pi \cdot RPM}{60}- Fc = centripetal force, in newtons (N)
- m = mass, in kilograms (kg)
- ω = angular speed, in radians per second (rad/s)
- RPM = revolutions per minute
- r = radius, in meters (m)
Using period
F_c = \frac{4\pi^2mr}{T^2}- Fc = centripetal force, in newtons (N)
- m = mass, in kilograms (kg)
- r = radius, in meters (m)
- T = period, or time for one full revolution, in seconds (s)
Use the linear speed tab when you know the object’s speed along the circular path. Use the RPM tab when you know rotation speed in revolutions per minute. Use the period tab when you know how long one complete revolution takes.
Common Input Conversions
These are the unit conversions applied before calculating force.
| Quantity | Input unit | SI conversion |
|---|---|---|
| Mass | 1 g | 0.001 kg |
| Mass | 1 lb | 0.45359237 kg |
| Velocity | 1 km/h | 0.277778 m/s |
| Velocity | 1 mph | 0.44704 m/s |
| Radius | 1 ft | 0.3048 m |
| Period | 1 min | 60 s |
Force Result Reference
| Result size | Equivalent form | Meaning |
|---|---|---|
| 1 N | 0.2248 lbf | A small force, about the weight of a 102 g mass under gravity. |
| 100 N | 22.48 lbf | About the weight of a 10.2 kg mass under gravity. |
| 1,000 N | 1 kN | A large force often written in kilonewtons. |
Example Problems
Example 1: Linear speed
A 2 kg object moves in a circle with a radius of 4 m at a speed of 6 m/s.
F_c = \frac{m v^2}{r}F_c = \frac{2 \cdot 6^2}{4} = 18\text{ N}The centripetal force is 18 N.
Example 2: RPM
A 0.5 kg mass rotates at 300 RPM at a radius of 0.2 m.
\omega = \frac{2\pi \cdot 300}{60} = 31.416\text{ rad/s}F_c = 0.5 \cdot 31.416^2 \cdot 0.2 = 98.7\text{ N}The centripetal force is about 98.7 N.
FAQ
Is angular force the same as centripetal force?
In this context, angular force means centripetal force: the inward force required for circular motion. In physics, “angular force” is not usually treated as a separate standard force. The actual force could come from tension, friction, gravity, a normal force, or another interaction, but its required inward value is the centripetal force.
Why does speed affect centripetal force so strongly?
Centripetal force depends on velocity squared. If you double the speed while mass and radius stay the same, the required force becomes four times larger. If you triple the speed, the required force becomes nine times larger.
What happens if the radius gets larger?
For the same linear speed, a larger radius reduces the required centripetal force because the turn is less sharp. For the same RPM or period, a larger radius increases the required force because the object travels faster around a larger circle in the same amount of time.
