Angular Acceleration to Linear Acceleration Calculator

Formula used

---

How to use this calculator

1. Enter the rotation radius and select its unit.
2. Enter angular acceleration and choose its unit.
3. Optionally enable angular velocity for additional outputs.
4. Select the angular velocity unit, then enter its value.
5. Press Calculate to see results above the form.
6. Use CSV or PDF to export the latest result.

Example data table

Professional article

1) Why convert angular to linear acceleration

Rotating systems often specify motion in angular terms, yet safety margins and component limits are usually linear. Tangential acceleration describes how quickly a point on a rotating body gains speed along its circular path. Converting α to a_t lets you compare motion directly with traction limits, belt slip thresholds, and allowable loads in test rigs.

2) Tangential component and measurement context

The tangential relationship a_t=αr is linear, so doubling radius doubles tangential acceleration for the same α. In practice, radius is the distance from the axis to the point of interest: a wheel tread, pulley groove, rotor tip, or sensor mount. For a 0.20 m radius, an α of 10 rad/s² yields 2.0 m/s² tangential acceleration.

3) When centripetal acceleration matters

If the point is also spinning with angular velocity ω, it experiences centripetal acceleration a_c=ω²r toward the axis. This term can dominate total acceleration at high ω. For ω=15 rad/s and r=0.20 m, a_c=45 m/s², far larger than the 2 m/s² tangential component in the same case.

4) Total linear acceleration and vector combination

Tangential and centripetal components are perpendicular for circular motion. The total magnitude is a=√(a_t²+a_c²). Using the previous values, √(2²+45²)=45.04 m/s². This helps engineers compare combined loading with accelerometer ranges and fatigue thresholds.

5) Unit choices and conversion reliability

The calculator accepts radius in meters, centimeters, millimeters, inches, or feet, and converts internally to meters. Angular acceleration can be entered as rad/s², deg/s², rev/s², or rpm/s. Angular velocity supports rad/s, deg/s, and rpm. Consistent conversion prevents silent scaling errors in reports.

6) Interpreting results in g

Expressing acceleration in multiples of standard gravity (g≈9.80665 m/s²) is convenient for shock and vibration work. For example, 45.04 m/s² corresponds to about 4.59 g. This framing helps when selecting sensors, mounts, and fixtures rated by g levels.

7) Typical application data points

Small lab turntables may run at 60 rpm (≈6.283 rad/s). At r=0.10 m, a_c=ω²r≈3.95 m/s² (~0.40 g). High-speed rotors at 3000 rpm (≈314.16 rad/s) and r=0.05 m produce a_c≈4934 m/s² (~503 g), emphasizing the importance of ω.

8) Best practices for accurate inputs

Measure radius to the exact point being evaluated, not the nominal component size. Use signed α when direction matters, but interpret magnitudes for stress checks. If ω varies during motion, evaluate at the peak ω for worst-case centripetal loading and export the results for traceability.

FAQs

1) What does this calculator compute?

It computes tangential linear acceleration from angular acceleration and radius. If you enable angular velocity, it also computes centripetal acceleration and the combined total magnitude.

2) Why is radius required?

Tangential acceleration scales with distance from the axis. The same angular acceleration produces higher linear acceleration at larger radii, so the radius identifies the point on the rotating body you care about.

3) When should I include angular velocity?

Include ω when you need centripetal loading or total acceleration, such as sensor range checks, bearing load estimates, or high-speed rotation where ω²r can dominate the acceleration magnitude.

4) Are tangential and centripetal accelerations added directly?

No. They are perpendicular in circular motion, so the total magnitude uses a vector combination: √(a_t² + a_c²). The calculator applies this automatically when ω is enabled.

5) What is “rpm/s” for angular acceleration?

It means the rotation rate changes by a certain number of revolutions per minute each second. The calculator converts rpm/s into rad/s² to ensure consistent physics units in the computations.

6) Why show values in g?

g units are common in vibration and shock specifications. Converting m/s² to g helps compare results with instrument ratings, packaging limits, and test standards stated as multiples of gravity.

7) Can the results be negative?

Tangential acceleration can be negative if you enter a negative angular acceleration, representing deceleration in your chosen direction. Centripetal and total magnitudes are reported as nonnegative values because they represent magnitudes.