Centripetal Force⚠ unverified
Physics / Mechanics · Compute the centripetal force for uniform circular motion
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| mass | mass | kg | 1.0 | Mass of the orbiting body |
| velocity | velocity | m/s | 1.0 | Tangential speed |
| radius | radius | m | 1.0 | Radius of the circular path |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Fc | N | Centripetal (radially inward) force, in newtons (N) |
The science & history
Understanding the Parameters
- $m$ — larger mass needs more force for the same path and speed.
- $v$ — force scales as $v^{2}$; high-speed turns demand large $F_c$.
- $r$ — tighter radius (smaller $r$) increases $F_c$ for fixed $v$.
- $F_c$ — must be supplied by real interactions; if they cannot, the path is not that circle.
Derivation (Approaching a Proof)
For uniform circular motion, velocity direction changes continuously. Geometry of the velocity vector over a short arc gives centripetal acceleration magnitude $a_c = v^{2}/r$ directed toward the centre. Newton’s second law radially: $F_{\mathrm{net},r} = m a_c$, hence
$$F_c = \frac{m v^{2}}{r}.$$
Equivalently $a_c = \omega^{2} r$ with $v = \omega r$. Related orbital balance: gravity providing $F_c$ yields Circular Orbital Velocity.
History
Huygens and Newton analysed circular motion; the modern “centripetal” terminology and $v^{2}/r$ form are standard Newtonian kinematics + dynamics.
Related Concepts: Newton's Second Law, Circular Orbital Velocity, Gravitational Force, Angular Momentum, Torque
Notes: Registry calculator centripetal-force (unverified). Uniform circular motion; net force
requirement, not a fundamental interaction by itself.