Calculator · Engineering Mechanics
Circular Motion Calculator
A particle moving on a circular path of fixed radius: speed, normal and tangential acceleration, and the vector form at a chosen angular position.
Path and motion
Positive counter-clockwise.
Measured counter-clockwise from +x.
Vectors at θ
Results
| Tangential speed v = r·ω | 6 m/s |
|---|---|
| Normal acceleration a_n = r·ω² | 18 m/s² |
| Tangential acceleration a_t = r·α | 8 m/s² |
| Total acceleration √(a_n² + a_t²) | 19.698 m/s² |
| Period T = 2π/|ω| | 2.0944 s |
| Frequency f = 1/T | 0.47746 Hz |
| Revolutions per minute | 28.648 rev/min |
| Position at θ | (2, 0) m |
| Velocity at θ | (0, 6) m/s |
| Normal acceleration at θ | (-18, 0) m/s² |
| Tangential acceleration at θ | (0, 8) m/s² |
Diagnostics
- · Info α ≠ 0: ω changes with time, so the period is the instantaneous value at this ω only.
Technical reference
v = r·ω
a_n = v²/r = r·ω²
a_t = r·α
|a| = √(a_n² + a_t²)
- r
- fixed path radius[m]
- ω
- angular velocity, +CCW[rad/s]
- α
- angular acceleration, +CCW[rad/s²]
- a_n
- centripetal (normal) acceleration, towards the centre[m/s²]
- a_t
- tangential acceleration[m/s²]
These relations are exact for a point particle on a fixed circular path — path kinematics only, with no mass or moment of inertia involved.
Assumptions
- · A point particle on a circular path of fixed radius — not a rotating rigid body.
- · Positive ω and α are counter-clockwise, the same convention as every Mechanics tool here.
- · Normal acceleration always points at the centre; tangential acceleration follows the sign of α.
- · Period and frequency describe the instantaneous ω only, and are undefined at ω = 0.
- · There is no handoff to the Particle Motion Lab: a constant-acceleration model cannot reproduce circular motion.